Theodore Kouassi BONI, Remi Kouadio KOUAKOU

6893

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.
Turkish Journal of Mathematics-Cover
  • ISSN: 1300-0098
  • Yayın Aralığı: 6
  • Yayıncı: TÜBİTAK
Arşiv
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