Lifespan for solutions to 4-th order hyperbolic systems with time dependent coefficients

Marras M.;Vernier Piro S.

2019-01-01

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Abstract

We study blow-up solutions of a nonlinear hyperbolic system of fourth order with time dependent coefficients under Dirichlet or Navier boundary conditions. We prove that under some restrictions on the data there exists a safe interval of existence of the solution and a lower bound of the lifespan is derived. The results are extended to a more general class of systems, where powers of the gradient of the solution are introduced. The proofs are based on some inequalities and coupled estimates techniques.