Stella Piro Vernier

Facoltà di Ingegneria e Architettura

CURRICULUM VITAE di

Stella Piro-Vernier

Indirizzo: Facoltà di Ingegneria e Architettura, Università of Cagliari

Via Marengo 2, 09123, Cagliari, Italy

e mail: svernier@unica.it

2018-2024 Professore a contratto presso la Facoltà di Ingegneria ed Architettura, Università di Cagliari
2006- 2017: Professore ordinario di Analisi Matematica presso l’Università di Cagliari, Dipartimento di Matematica e Informatica
2012/2015 Direttore del Dipartimento di Matematica e Informatica Università di Cagliari .

2004/2007: Direttore dell’ Area 01 : Dipartimento di Matematica e Informatica

2004/2007: vice Direttore del Dipartimento di Matematica e Informatica Università di Cagliari .
2002 – 2018 : direttore Unità di ricerca INDAM, Università di Cagliari.
1997/2004 : Direttore del Dipartimento di Matematica e Informatica Università di Cagliari .

Attività scientifica (2000- 2023)

Ricerca scientifica:

Nonlinear elliptic equations: eigenvalues of p-Laplace-type equations (in collaborazione con Porru, Marras).

Nonlinear parabolic equations and systems, models in Physics, Chemestry and Biology (in collaborazione con Marras, Viglialoro)

Qualitative properties of the solutions: global existence, blow-up in finite time, decay estimates (in collaborazione con Marras, Philippin).

Behavior of solutions to degenerate and singular parabolic equations (in collaborazione con Marras, Ragnedda, Vespri)

Lista degli articoli pubblicati dal 2000 a oggi.

( per una lista completa vedi: http://www.ams.org/mathscinet/ o www.scopus.com)

M. Marras, S. Vernier-Piro and T. Yokota,"Finite time blow up in Keller Segel with flux limitation and source term" NoDEA (2023) 30:65.

M.Marras, F.Ragnedda, S.Vernier-Piro and V.Vespri ,"Holder estimates of weak solutions to degenerate chemotaxis systems with a source term", Journal of Differential Equations 366 (2023) 42-70.

M. Marras, S. Vernier-Piro and T. Yokota, "Blow-up phenomena for a chemotaxis system with flux limitation" J. Math. Anal. Appl. 515 (2022) 126376.

M.Marras- S. Vernier-Piro," A class of fourth-order parabolic systems with time dependent coefficients with blow-up solutions"(Submitted).

Stella Vernier-Piro, “Finite time blow up in a fourth order dispersive wave equation with nonlinear damping and non-local source”, Axioms 2022, 11, 212. https:// doi.org/10.3390/axioms11050212

M.Marras , S. Vernier Piro, Finite time collapse in chemotaxis systems with logistic-type superlinear source, Math. Meth. Appl. Sci. (2020)

M.Marras , S. Vernier Piro, G. Viglialoro, Decay of the solutions to a general model of chemotaxis, DCDS-S, February 2020, 13(2): 257-268. doi: 10.3934/dcdss.2020014

M.Marras , S. Vernier Piro, A note on a class of 4th order hyperbolic problems with weak and strong damping and superlinear source term, DCDS-S (2020)13(7): 2047-2055 doi: 10.3934/dcdss.2020157

M.Marras , S. Vernier Piro, Lifespan for solutions to 4-th order hyperbolic systems with time dependent coefficients, J. Math. Anal. Appl. vol.480, Issue 1, (2019) doi.org/10.1016/j.jmaa.2019.123387

F.Ragnedda, S.Vernier Piro and V.Vespri , Holder regularity for bounded solutions to a class of anisotropic operators, manuscripta mathematica, 158(3), 421-439 (2019), https://doi.org/10.1007/s00229-018-1034-z

V. Bogelein, F.Ragnedda, S.Vernier Piro and V.Vespri , Moser- Nash kernel estimates for degenerate parabolic equations, J. Funct. Anal. (2017), dx.doi.org/10.1016/jfa.2016.12.023

M.Marras , S. Vernier Piro. G. Viglialoro, Blow-up phenomena for nonlinear pseudo-parabolic equations with gradient term, DCDS-B (2017)

M.Marras , S. Vernier Piro, Blow-up time estimates in nonlocal reaction-diffusion systems under various boundary conditions, Boundary Value Problems 2017 (1), 2

M.Marras, S.Vernier Piro, G. Viglialoro, “Blow-up and phenomena in chemotaxis system with a source term. ” Math. Meth. Appl. Sciences, 39 (2016), n.11, 2787-2798.

G. Philippin, S.Vernier Piro, “Behaviour in time of solutions to a class of fourth order evolution equations. ” J. Math. Anal. Appl. 436 (2016), n.2, 718-728.

Youshan Tao, S.Vernier Piro, “Explicit lower bound of blow-up time in a fully parabolic chemotaxis system with nonlinear cross-diffusion. ”
J. Math. Anal. Appl. 436 (2016), n.1, 16-28 .

G. Philippin, S.Vernier Piro, “Lower bound for the lifespan of solutions for a class of fourth order wave equations. ”
Appl. Math. Letters, 50 (2015), 141-145 doi.org/10.1016/j.aml.2015.06.01 .

M.Marras, S.Vernier Piro, G. Viglialoro, “Lower bounds for blow-up in a parabolic-parabolic in a Keller-Segel system. “Discete Contin. Dyn. Syst.2015,
Dynamical Systems, Differential Equations and Applications, 10th AIMS Conference, pp. 809-816. doi:10.3934/proc.2015.0809.

M.Marras , S.Vernier Piro, “Blow-up and decay bounds in Hamilton Jacobi type problem. ”
Advances in Dynamical Systems and Applications, 9 (2),(2014), 213-219.

M.Marras , S.Vernier Piro, G.Viglialoro “Lower bounds for blow-up time in a parabolic problem with a gradient term under varius boundary conditions. ”
Kodai Math. Journal, 37 (2014), n.3, 532-543 ISSN: 0386-5991.

M.Marras , S.Vernier Piro, “Reaction-diffusion problems under non-local boundary conditions with blow-up solutions. ”
Journal of Inequalities and Applications (2014), 167-177, DOI: 10.1186/1029-242X-2014-167.

M.Marras , S.Vernier Piro, “Explicit estimates for blow-up solutions to parabolic systems with time dependent coefficients. ”
Comtes Rendus de l’Academie Bulgare des Sciences, (2014) vol. 67, 459-466, ISSN: 1310-1331 .

M.Marras , S.Vernier Piro, “On global existence and bounds for blow-up time in nonlinear parabolic problems with time dependent coefficients”
Discrete and Continuous Dynamical Systems (2013) vol. suppl. 535-544, ISSN: 1078-0947

M.Marras, G.Porru, S. Vernier – Piro, “Optimization problems for eigenvalues of p-Laplace equations. ” J. Math. Anal. Appl. 398 (2013) 766-775, ISSN: 0022-247X .

T. Gramchev, M.Marras and S. Vernier – Piro, “On extinction phenomena for parabolic system ” Springer Proceedings in Mathematics and Statistics, Vol. 47, Pinelas, Sandra; Chipot, Michel; Dosla, Zuzana (Eds.) (2013) .

F.Ragnedda, S.Vernier Piro and V.Vespri, “Pointwise estimates for the fundamental solutions of class of singular parabolic problems. ”
Journal d’Analyse Mathematique, (2013), vol. 121, p. 235-253, ISSN: 0021-7670, doi: 10.1007/s11854-013-0034-x .

M.Marras, S. Vernier – Piro, “Blow-up phenomena in reaction-diffusion systems” DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, Volume 32, Number 11, (2012) .

F.Ragnedda, S.Vernier Piro, V.Vespri, “The asymptotic profile of solutions of a class of singular parabolic equations. “, Progress in Nonlinear Differential Equations and Their Applications, Vol.60, 577-589 (2011) Springel Basel AG)

M.Marras, S. Vernier – Piro, “Bounds for blow-up time in nonlinear parabolic system” DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, Suppement 2011 (2011) 1025-1031.

F.Ragnedda, S.Vernier Piro, V.Vespri, “Large time behaviour of solutions to a class of non-autonomous degenerate parabolic equations. ”
Math. Ann. 348 (2010), no. 4, 779–795

L.E.Payne, G.Philippin, S. Vernier Piro, ” Blow-up phenomena for a semilinear heat equation with nonlinear boundary condition, II ”
Nonlinear Analysis 73 (2010), pp. 971-978.

L.E.Payne, G.Philippin, S. Vernier Piro, ” Blow-up phenomena for a semilinear heat equation with nonlinear boundary condition, I ”
Z. Angew. Math. Phys., 61, 999-1007, (2010).

M.Marras, S. Vernier – Piro, “Continuous dependence results for parabolic problems under Robin boundary conditions“Numer. Funct. Anal. Optim. 20 (2009), no. 1-2, 121- 135).

F.Ragnedda, S.Vernier Piro, V.Vespri, ” Asymptotic time behaviour for non-autonomous degenerate parabolic problems with forcing term.”
Nonlinear Analysis 71 (2009) e2316 – e2321

G. Philippin, V. Proytcheva, S. Vernier-Piro “Continous dependance result for a class of nonlinear heat equations in a cylindrical region”
Math. Meth. Appl. Sci.,2009, Vol.32, pp330-345.

S. Vernier – Piro, “Qualitative properties for solutions of reaction-diffusion parabolic systems and their gradients”
Nonlinear Analysis, 68, (2008), 1775-1783

M. Marras – S. Vernier – Piro, “Exponential decay bounds for nonlinear heat problems with Robin boundary conditions”
Zeitschrift fur Angew. Math.Phys, 59, n°5, (2008), 766-779

M. Marras – S. Vernier – Piro, “Blow up and decay bounds in quasilinear parabolic problems”
Discrete and continuous dynamical systems, vol.suppl.(2007), 704-712

M. Marras – S. Vernier – Piro, “Maximum principles and decay estimates for parabolic systems under Robin Boundary conditions”
Differential & Difference Equations and Appl., Hindawi Publ. Corp., (2006) 767-773

L.E. Payne – G. Philippin- S. Vernier – Piro, “Decay bounds for solutions of second order parabolic problems and their derivatives IV”
Applicable Analysis, vol. 85, n. 1-3 (2006) 293-302

L.E. Payne – G. Philippin- S. Vernier – Piro, “Blow-up, decay bounds and continuous dependence inequalities for a class of quasilinear parabolic problems“, Math. Meth. Appl. Sci.,29 (2006) 281-295.

S. Vernier – Piro, “Some decay results for solutions of parabolic problems” Le Matematiche, vol.LX, (2005), 457-462

M. Marras – S. Vernier – Piro, “Upper and lower solutions for quasilinear parabolic boundary value problems” Zeitschrift fur Angew. Math.Phys,56, (2005), 1-15.

G. Porru, A. Safoui, S. Vernier – Piro, “Best Possible Maximum principles for fully nonlinear elliptic partial differential equations” “Z. Anal. Anwend. 25 (2006), no. 4, 421-434.

S. Vernier – Piro, “Applications of “Best Possible Maximum principles” to parabolic problems in non convex domains“, Dynamic Systems Applications, vol. 4 (2004), 245-250) .

C. Bandle, S. Vernier-Piro, “Estimates for solution of quasilinear problems with dead cores”
Z. Angew. Math. Phys., vol.54, no. 5, (2003), 815-821.

C. Van der Mee, S. Vernier-Piro, “Traveling Waves for Solid-gas Reaction – diffusion Systems” Discrete and Continuous Dynamical Systems, suppl. vol. “Dynamical Systems and Differential Equations ” (2003), 872-879.

C.Van der Mee, S.Vernier-Piro, “Dead cores for parabolic reaction diffusion problems”
Dynamics of Continuous, Discrete and Impulsive Systems, serie A: Math. Analysis (2003), 10, 139-147.

M. Marras, S. Vernier-Piro, “Sharp upper and lower solutions in some parabolic problems”
Nonlinear Funct. Anal. Optim. 23 (2002), no. 3, 483-495.

G. Philippin- S. Vernier – Piro, “Comparison results for solutions of reaction diffusion problems“, Glasg. Math. J. 44 (2002), no 5-6, 609-621.

C.Van der Mee, S.Vernier-Piro, “Dead cores for time dependent reaction diffusion equations“, Nonlinear Analysis, 47, (2001), 2113-2123.

G.Philippin- S. Vernier-Piro, “Decay estimates for solutions of a class of parabolic problems arising in filtration in porous media“, Boll. Unione Matem. Ital. (8) 4 (2001), 473-481.

I. Stakgold, C. Van der Mee, S. Vernier-Piro, “Traveling waves for gas-solid reactions in porous medium with porosity change“, Dynam. Systems Appl. 10, (2001) no 4, 589-598.

G.Philippin- S.Vernier-Piro, “Applications of the maximum principles to a variety of problems involving elliptic and parabolic equations“, Nonlinear Analysis, 47, (2001), 661-679.

G. Philippin- S. Vernier – Piro, “Decay estimates for solutions of various parabolic problems“, Mat. Contemp. 19, (2000), 89-103.

Nel Comitato scientifico dei convegni :

“Partial Differential equations and relative topics” Alghero, September 12-16, 2016

http://www.dma.unina.it/ferone/alghero2016

“Trends in Nonlinear Analysis” Cagliari, March 21-22, 2014

http://people.unica.it/stellapiro/news/

“ Elliptic and parabolic problems: qualitative properties of solutions” .

Cagliari, Sept. 24-25, 2004. http://riemann.unica.it/Philippin

“Elliptic and Parabolic Problems” to celebrate the 80th anniversary of Larry Payne.

Cagliari, June 5-7 2003. (http://riemann.unica.it/Payne)

Workshop “Evolution equations : perturbative methods, regularity and qualitative proprieties of solutions” Cagliari , July 12-14, 2001
“Perturbative Methods for Partial Differential Equations and Dynamic Systems, Cagliari , October 23-28 , 2000.”

– Invited speaker in diverse conferenze in Italia e all’estero:

2016	2022 - IV Workshop on Trends in Nonlinear Analysis, Cagliari: Sept. 13 - 14, 2022- talk " Behavior in time of the solutions of Keller-Segel system with flux limitation and source term" 2019- Turkey-Italy Colloquium on Applied Analysis and Differential Equations July 10-11, 2019 Ankara- talk: “Estimates for solutions to a class of nonlinear degenerate parabolic problems.” 2018- Two Nonlinear Days in Perugia on the occasion of Patrizia Pucci’s 65th birthday Perugia 11-12 January 2018. talk "Regularity estimates for solutions to a class of anisotropic elliptic equations" 2018- 12th AIMS Conference on Dynamical Systems, Differential Equations and Applications. July 5 – July 9 , 2018, Taipei, Taiwan 1st talk: Blow-up phenomena in hyperbolic 4th order equations. 2nd talk. Sharp pointwise estimates for solutions to nonlinear degenerate parabolic equation 2017- A Life in Mathematics: Conference in memory of Todor V. Gramch Generalized functions, Microlocal analysis, PDEs and Dynamical systems, 1- 3 Febbraio 2017, Dipartimento di Matematica, Universita' di Torino, talk "Blow-up phenomena in wave theory" 2017- Workshop”Harnack Inequalities and Nonlinear Operators” June 19 – June 23 , 2017, Cortonatalk: Regularity estimates for solutions to a class of anisotropic elliptic equations. 11th AIMS Conference on Dynamical Systems, Differential Equations and Applications. July 1 – July 5, 2016, Orlando, Florida, USA : 1st talk: Explicit lower bound of blow-up time to a parabolic chemotaxis system with nonlinear cross-diffusion, 2nd talk. Behaviour in time of solutions to a class of fourth order evolution equations Workshop “The total variation flow and related nonlinear evolution problems”, University of Salzburg, July 11-15, 2016, talk: “ Sharp pointwise estimates for solutions to nonlinear degenerate parabolic equations” 2014 – 10th AIMS Conference on Dynamical Systems, Differential Equations and Applications, Madrid, July 7 – 11, 2014- 1st talk : Blowing up and global solutions of a nonlinear parabolic problem. 2nd talk: Blow-up solutions in a Keller-Segel type system modelling the chemotaxis phenomenon. 2013- Conference on Nonlinear Evolutions Equations and Linear Algebra (to celebrate the 60th birthday of Cornelis Van der Mee) Cagliari, Italy, Sept. 2-5, 2013 – talk “A model of chemotaxis with blow-up solutions.”

2013	SYMPOSIUM ON DIFFERENTIAL AND DIFFERENCE EQUATIONS Bayrischzell, Bavaria, Germany, sept.1-5, 2013 -talk “A Keller -Siegel system with blow-up solutions.” “

2012	VII Congreso Italo-Latinoamericano de Matematica Aplicada e Industrial (VII ITLA 2012) , Rosario (Argentina) dal 17 al 21 Dicembre 2012, talk: “Blow up solutions in nonlinear parabolic problems.”

2012	9th AIMS Conference on Dynamical Systems, Differential Equations and Applications, July 1 – 5, 2012. Orlando, Florida, USA. Talk “Pointwise estimates for solutions to a class of singular parabolic equations”

2011	International Conference on Differential & Difference Equations and Applications, Department of Mathematics, Azores University, Ponta Delgada, Portugal, July 4 – 8 2011. Talk “Bounds to blow-up time in nonlinear parabolic systems”

2010	The 8th AIMS International Conference on Dynamical Systems, Differential Equations and Applications, Dresden, May 24-28, 2010, Talk “Blow-up phenomena for a semilinear heat equation with nonlinear boundary condition”

2007	Fourth Inter. Conference of Applied Mathematics, Plovdiv (Bulgaria), August 12-18, 2007, talk”Exponential decay bounds for nonlinear heat problems with Robin boundary conditions “

2005	Conference on Differential & Difference Equations and Applications, Florida Institute of Technology, Melbourne, Florida, August 1-5, 2005, talk “Bounds for solutions of nonlinear parabolic systems “

2005	International Conference on “Free Boundary Problems. Theory and Applications”, Coimbra,Portogallo, June 7-12, 2005, talk “Dead cores for Parabolic Reaction-Diffusion Problems “

2003	International Conference on “Dynamics Systems and Applications”, Atlanta, May 20-24, 2003, talk”Optimal upper and lower solutions in parabolic problems “

2002	The Fourth International Conference on Dynamics Systems and Differential Equations, May 24-27, 2002, Wilmington, NC USA, talk : “Travelling waves for solid gas reaction under condition of constant gas flux”

2001	International Conference on Dynamics of Continuous, Discrete and Impulsive Systems, London, Ontario, Canada, July 27-31, 2001, talk “Dead cores for Parabolic reaction diffusion Systems”


Visiting
2014 Donghua University, Shanghai, Cina (prof. Youshan Tao) – Blow-up solutions in a Keller-Segel type system modelling the chemotaxis phenomenon.
2013	Università di Laval , Quebec , Canada (prof. Gerard Philippin ) – Nonlinear Parabolic systems with blow-up solutions.

2011	Università di Laval , Quebec , Canada (prof. Gerard Philippin ) – Blow up solutions to nonlinear parabolic problems.
2010 Universite’ Nancy (Nancy, France), prof. A. Henrot ,prof.G. Philippin
2009	Università di Laval , Quebec , Canada (prof. Gerard Philippin ) – Upper and lower bounds for blow up time of solutions to nonlinear parabolic problems.

2007	Università di Laval , Quebec , Canada (prof. Gerard Philippin ) – Continuous dependance results for a class of nonlinear heat problems in cylindrical regions.

2006	Dipartimento di Matematica, Basilea, Svizzera (Prof. Catherine Bandle) – Problemi parabolici quasilineari con dead core.

2005	Università di Laval, Quebec, Canada (prof. Gerard Philippin) – Proprietà qualitative delle soluzioni di problemi parabolici.

2003	Università di Laval, Quebec, Canada (prof. Gerard Philippin) – Stime decrescenti nel tempo per soluzioni di problemi parabolici del 2° ordine in domini non convessi.

2002	Dipartimento di Matematica, Basilea, Svizzera (prof. Catherine Bandle) – Stime di soluzioni di problemi ellittici quasilineari con dead cores.

2001	Dipartimento di Matematica, Basilea, Svizzera (prof. Catherine Bandle) – Conferenza: Principi di massimo in spazi a curvatura costante.

2001	Ecole Politechnique Federal de Lausanne, Svizzera (prof. C.Stuart e G.Philippin) – Conferenza: Sopra e sotto-soluzioni per problemi parabolici semilineari.

2001	Università del Delaware, USA (prof. Ivar Stakgold) – Conferenza: Dead cores per sistemi parabolici tipo reazione diffusione.

– Referee in diverse riviste internazionali

– Advisor di tesi di dottorato

– Coordinatore di progetti scientifici a Cagliari.

Attività didattica fino al 2017.

Docente dei corsi di Analisi Matematica in Facoltà di Ingegneria ed Architettura.

Docente di Analisi Superiore per gli studenti di Laurea Magistrale, corso di Laurea in Matematica, Facoltà di Scienze.

Docente nei corsi di dottorato di ricerca in Matematica: Maximum principles for elliptic and parabolic equations.

(aggiornato al 10 Agosto 2023)

Attività didattica dal 2018-2024.

Docente del corso di Analisi Matematica II ccs EEI

Attività didattica dal 2022-2024.

Docente del corso di Matematica, ccs TET

---------------------------------------------------------

CURRICULUM VITAE

Stella Piro-Vernier

Academic address: Faculty of Engineering and Architecture, University of Cagliari

Via Marengo 2, 09123, Cagliari, Italy

e-mail: svernier@unica.it

2018-2024 Professore a contratto, Faculty of Engineering and Architecture.
2006- 2017: FULL PROFESSOR in Mathematics at the University of Cagliari, Department of Mathematics and Computer Sciences
2012/2015 Head of Department of Mathematics and Computer Sciences University of Cagliari .

2004/2007: Head of Area 01 : Mathematics and Computer Sciences
2004/2007: vice head Department of Mathematics and Computer Sciences
2002 – present : head Unità di ricerca INDAM, University of Cagliari.
1997/2004 : Head of Department of Mathematics and Computer Sciences

Scientific activity (2000- present)

Scientific research:

Nonlinear elliptic equations: eigenvalues of p-Laplace-type equations (Porru, Marras).

Nonlinear parabolic equations and systems, models in Physics, Chemestry and Biology (Marras, Viglialoro)

Qualitative properties of the solutions: global existence, blow-up in finite time, decay estimates (Marras, Philippin).

Behavior of solutions to degenerate and singular parabolic equations (Marras, Ragnedda, Vespri)

List of scientific publications (2000-present)

( for the complete list see: http://www.ams.org/mathscinet/ or www.scopus.com)

M. Marras, S. Vernier-Piro and T. Yokota,"Finite time blow up in Keller Segel with flux limitation and source term" , NoDEA (2023) 30:65

M.Marras, F.Ragnedda, S.Vernier-Piro and V.Vespri ,"Holder estimates of weak solutions to degenerate chemotaxis systems with a source term", Journal of Differential Equations 366 (2023) 42-70.

M. Marras, S. Vernier-Piro and T. Yokota, "Blow-up phenomena for a chemotaxis system with flux limitation" J. Math. Anal. Appl. 515 (2022) 126376.

M.Marras- S. Vernier-Piro," A class of fourth-order parabolic systems with time dependent coefficients with blow-up solutions"(Submitted).

Stella Vernier-Piro, “Finite time blow up in a fourth order dispersive wave equation with nonlinear damping and non-local source”, Axioms 2022, 11, 212. https:// doi.org/10.3390/axioms11050212

M.Marras , S. Vernier Piro, Finite time collapse in chemotaxis systems with logistic-type superlinear source, Math. Meth. Appl. Sci. (2020)

M.Marras , S. Vernier Piro, G. Viglialoro, Decay of the solutions to a general model of chemotaxis, DCDS-S, February 2020, 13(2): 257-268. doi: 10.3934/dcdss.2020014

M.Marras , S. Vernier Piro, A note on a class of 4th order hyperbolic problems with weak and strong damping and superlinear source term, DCDS-S (2020)13(7): 2047-2055 doi: 10.3934/dcdss.2020157

M.Marras , S. Vernier Piro, Lifespan for solutions to 4-th order hyperbolic systems with time dependent coefficients, J. Math. Anal. Appl. vol.480, Issue 1, (2019) doi.org/10.1016/j.jmaa.2019.123387

F.Ragnedda, S.Vernier Piro and V.Vespri , Holder regularity for bounded solutions to a class of anisotropic operators, manuscripta mathematica, 158(3), 421-439 (2019), https://doi.org/10.1007/s00229-018-1034-z

V. Bogelein, F.Ragnedda, S.Vernier Piro and V.Vespri , Moser- Nash kernel estimates for degenerate parabolic equations, J. Funct. Anal. (2017), dx.doi.org/10.1016/jfa.2016.12.023

M.Marras , S. Vernier Piro. G. Viglialoro, Blow-up phenomena for nonlinear pseudo-parabolic equations with gradient term, DCDS-B (2017)

M.Marras , S. Vernier Piro, Blow-up time estimates in nonlocal reaction-diffusion systems under various boundary conditions, Boundary Value Problems 2017 (1), 2

M.Marras, S.Vernier Piro, G. Viglialoro, “Blow-up and phenomena in chemotaxis system with a source term. ” Math. Meth. Appl. Sciences, 39 (2016), n.11, 2787-2798.

G. Philippin, S.Vernier Piro, “Behaviour in time of solutions to a class of fourth order evolution equations. ” J. Math. Anal. Appl. 436 (2016), n.2, 718-728.

Youshan Tao, S.Vernier Piro, “Explicit lower bound of blow-up time in a fully parabolic chemotaxis system with nonlinear cross-diffusion. ”J. Math. Anal. Appl. 436 (2016), n.1, 16-28 .

G. Philippin, S.Vernier Piro, “Lower bound for the lifespan of solutions for a class of fourth order wave equations” Appl. Math. Letters, 50 (2015), 141-145 doi.org/10.1016/j.aml.2015.06.01 .

M.Marras , S.Vernier Piro, “Blow-up and decay bounds in Hamilton Jacobi type problem. ”
Advances in Dynamical Systems and Applications, 9 (2),(2014), 213-219.

M.Marras , S.Vernier Piro, “On global existence and bounds for blow-up time in nonlinear parabolic problems with time dependent coefficients”
Discrete and Continuous Dynamical Systems (2013) vol. suppl. 535-544, ISSN: 1078-0947

M.Marras, G.Porru, S. Vernier – Piro, “Optimization problems for eigenvalues of p-Laplace equations. ” J. Math. Anal. Appl. 398 (2013) 766-775, ISSN: 0022-247X .

T. Gramchev, M.Marras and S. Vernier – Piro, “On extinction phenomena for parabolic system ” Springer Proceedings in Mathematics and Statistics, Vol. 47, Pinelas, Sandra; Chipot, Michel; Dosla, Zuzana (Eds.) (2013) .

F.Ragnedda, S.Vernier Piro and V.Vespri, “Pointwise estimates for the fundamental solutions of class of singular parabolic problems. ”
Journal d’Analyse Mathematique, (2013), vol. 121, p. 235-253, ISSN: 0021-7670, doi: 10.1007/s11854-013-0034-x .

M.Marras, S. Vernier – Piro, “Blow-up phenomena in reaction-diffusion systems” DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, Volume 32, Number 11, (2012) .

F.Ragnedda, S.Vernier Piro, V.Vespri, “The asymptotic profile of solutions of a class of singular parabolic equations. “, Progress in Nonlinear Differential Equations and Their Applications, Vol.60, 577-589 (2011) Springel Basel AG)

M.Marras, S. Vernier – Piro, “Bounds for blow-up time in nonlinear parabolic system” DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, Suppement 2011 (2011) 1025-1031.

F.Ragnedda, S.Vernier Piro, V.Vespri, “Large time behaviour of solutions to a class of non-autonomous degenerate parabolic equations.” Math. Ann. 348 (2010), no. 4, 779–795

L.E.Payne, G.Philippin, S. Vernier Piro, ” Blow-up phenomena for a semilinear heat equation with nonlinear boundary condition, II ” Nonlinear Analysis 73 (2010), pp. 971-978.

L.E.Payne, G.Philippin, S. Vernier Piro, ” Blow-up phenomena for a semilinear heat equation with nonlinear boundary condition, I ” Z. Angew. Math. Phys., 61, 999-1007, (2010).

M.Marras, S. Vernier – Piro, “Continuous dependence results for parabolic problems under Robin boundary conditions“ Numer. Funct. Anal. Optim. 20 (2009), no. 1-2, 121- 135).

F.Ragnedda, S.Vernier Piro, V.Vespri, ” Asymptotic time behaviour for non-autonomous degenerate parabolic problems with forcing term.” Nonlinear Analysis 71 (2009) e2316 – e2321

G. Philippin, V. Proytcheva, S. Vernier-Piro “Continous dependance result for a class of nonlinear heat equations in a cylindrical region” Math. Meth. Appl. Sci.,2009, Vol.32, pp330-345.

S. Vernier – Piro, “Qualitative properties for solutions of reaction-diffusion parabolic systems and their gradients” Nonlinear Analysis, 68, (2008), 1775-1783

M. Marras – S. Vernier – Piro, “Exponential decay bounds for nonlinear heat problems with Robin boundary conditions” Zeitschrift fur Angew. Math.Phys, 59, n°5, (2008), 766-779

M. Marras – S. Vernier – Piro, “Blow up and decay bounds in quasilinear parabolic problems”
Discrete and continuous dynamical systems, vol.suppl.(2007), 704-712

L.E. Payne – G. Philippin- S. Vernier – Piro, “Decay bounds for solutions of second order parabolic problems and their derivatives IV” Applicable Analysis, vol. 85, n. 1-3 (2006) 293-302