Blow-up time for a semilinear parabolic equation with variable reaction
In this paper, we address the solution of a semilinear heat equation with variable reaction subject to Dirichlet boundary conditions and nonnegative initial datum. Under some assumptions, we show that the solution of the above problem blows up in a finite time, and its blow-up time goes to that of the solution of a certain differential equation. Finally, we give some numerical results to illustrate our analysis.
Anahtar Kelimeler:
Semilinear parabolic equation, blow-up, numerical blow-up time
Blow-up time for a semilinear parabolic equation with variable reaction
In this paper, we address the solution of a semilinear heat equation with variable reaction subject to Dirichlet boundary conditions and nonnegative initial datum. Under some assumptions, we show that the solution of the above problem blows up in a finite time, and its blow-up time goes to that of the solution of a certain differential equation. Finally, we give some numerical results to illustrate our analysis.
Keywords:
Semilinear parabolic equation, blow-up, numerical blow-up time,
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- (3) In Figure 3, we plot the evolution of the discrete solution for M = 10 , I = 16 and ε = 1. (4) In Figure 4, we plot the evolution of the discrete solution for M = 20 , I = 16 and ε = 1.
- ISSN: 1300-0098
- Yayın Aralığı: Yılda 6 Sayı
- Yayıncı: TÜBİTAK
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