Turkish Journal of Mathematics
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.
DOI
10.3906/mat-2103-11
Keywords
Parabolic problem, heat equation, nonlinear boundary condition, blow-up
First Page
2406
Last Page
2418
Recommended Citation
LAMAIZI, A, ZEROUALI, A, CHAKRONE, O, & KARIM, B (2021). Global existence and blow-up of solutions for parabolic equations involving the Laplacian under nonlinear boundary conditions.. Turkish Journal of Mathematics 45 (6): 2406-2418. https://doi.org/10.3906/mat-2103-11
