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Global existence and blow-up of solutions for parabolic equations involving the Laplacian under nonlinear boundary conditions.
2021
Journal:  
Turkish Journal of Mathematics
Author:  
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:

null
2021
Journal:  
Turkish Journal of Mathematics
Author:  
DOI:  
10.3906/mat-2103-11
0
2021
Journal:  
Turkish Journal of Mathematics
Author:  
DOI:  
10.3906/mat-2103-11
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Turkish Journal of Mathematics

Field :   Fen Bilimleri ve Matematik

Journal Type :   Uluslararası

Metrics
Article : 2.274
Cite : 712
2023 Impact : 0.039
Details
Turkish Journal of Mathematics