Numerical quenching versus blow-up for a nonlinear parabolic equation with nonlinear boundary outflux
| Autor: | Kidjegbo Augustin Toure, Gozo Yoro, Kouakou Cyrille N'dri |
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| Rok vydání: | 2020 |
| Předmět: | |
| Zdroj: | Advances in Mathematics: Scientific Journal. :151-171 |
| ISSN: | 1857-8438 1857-8365 |
| Popis: | In this paper, we study numerical approximations for positive solutions of a semilinear heat equations, $u_{t}=u_{xx}+u^{p}$, in a bounded interval $(0,1)$, with a nonlinear flux boundary condition at the boundary $u_{x}(0,t)=0$, $u_{x}(1,t)=-u^{-q}(1,t)$. By a semi-discretization using finite difference method, we get a system of ordinary differential equations which is expected to be an approximation of the original problem. We obtain some conditions under which the positive solution of our system quenches or blows up in a finite time and estimate its semidiscrete blow-up and quenching time. We also estimate the semidiscrete blow-up and quenching rate. Finally, we give some numerical results to illustrate our analysis. |
| Databáze: | OpenAIRE |
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