Simultaneous and non-simultaneous quenching for a coupled semilinear parabolic system in a n-dimensional ball with singular localized sources
In this paper, we investigate a coupled semilinear parabolic system with singular localized sources at the point x0: ut−Δu=af(v(x0,t)), vt−Δv=bg(u(x0,t)) for x∈B1(x0) and t∈(0,T) with the Dirichlet boundary condition, where a and b are positive real numbers, B1(x0) is a n-dimensional ball with the c...
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| Format: | Article |
| Language: | English |
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AIMS Press
2021-05-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2021447?viewType=HTML |
| Summary: | In this paper, we investigate a coupled semilinear parabolic system with singular localized sources at the point x0: ut−Δu=af(v(x0,t)), vt−Δv=bg(u(x0,t)) for x∈B1(x0) and t∈(0,T) with the Dirichlet boundary condition, where a and b are positive real numbers, B1(x0) is a n-dimensional ball with the center and radius being x0 and 1, and the nonlinear sources f and g are positive functions such that they are unbounded when u and v tend to a positive constant c, respectively. We prove that the solution (u,v) quenches simultaneously and non-simultaneously under some sufficient conditions. |
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| ISSN: | 2473-6988 |