Global existence and blow-up of solutions for parabolic equations involving the Laplacian under nonlinear boundary conditions.

Authors

ANASS LAMAIZI
ABDELLAH ZEROUALI
OMAR CHAKRONE
BELHADJ KARIM

DOI

10.3906/mat-2103-11

Abstract

This paper is concerned with the existence and blow-up of solutions to the following linear parabolic equation: $ ~~ u_t - \Delta u +u = 0 \quad \text{ in } \Omega \times (0,T) $, under nonlinear boundary condition in a bounded domain $ \Omega \subset \mathbb{R}^n $, $n \geq 1$, with smooth boundary. We obtain a threshold result for the global existence of solutions, next we shall prove the existence time $T$ of solution is finite when the initial energy satisfies certain condition.

Keywords

Parabolic problem, heat equation, nonlinear boundary condition, blow-up

First Page

2406

Last Page

2418

Recommended Citation

LAMAIZI, ANASS; ZEROUALI, ABDELLAH; CHAKRONE, OMAR; and KARIM, BELHADJ (2021) "Global existence and blow-up of solutions for parabolic equations involving the Laplacian under nonlinear boundary conditions.," Turkish Journal of Mathematics: Vol. 45: No. 6, Article 4. https://doi.org/10.3906/mat-2103-11
Available at: https://journals.tubitak.gov.tr/math/vol45/iss6/4