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.
Sharp upper and lower solutions in some parabolic problems
MARRAS, MONICA;PIRO, STELLA
2002-01-01
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.
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