Asymptotic analysis for the strip problem related to a parabolic third - order operator

TL;DR

This paper analyzes the asymptotic behavior of solutions to a boundary value problem for a third-order nonlinear parabolic equation, providing explicit solutions in the linear case and estimates for the nonlinear case.

Contribution

It offers a detailed asymptotic analysis of a third-order nonlinear parabolic boundary value problem, including explicit solutions for the linear case and convergence estimates for the nonlinear case.

Findings

Explicit Fourier series solution for the linear case

Asymptotic behavior characterized through series estimates

Applicable to dissipative models described by the equation

Abstract

Aim of this paper is the qualitative analysis of a boundary value problem for a third order non linear parabolic equation which describes several dissipative models. When the source term is linear, the problem is explictly solved by means of a Fourier series with properties of rapid convergence. In the non linear case, appropriate estimates of this series allow to deduce the asymptotic behaviour of the solution.