Sharp upper and lower solutions in some parabolic problems

MARRAS, MONICA;PIRO, STELLA

2002-01-01

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Abstract

In this paper we construct upper and lower solutions for a class of parabolic initial-boundary value problems in terms of the solution $\psi(x)$ of the St-Venant problem and first eigenvalue problem. These bounds are sharp in the sense that they coincide with the exact solution in particular situations.