A semilinear heat equation with concave-convex nonlinearity
In this paper, we are interested in the parabolic equation u_t − ∆u = λu^q + u^p in a bounded domain of IR^N, with the Dirichlet boundary condition and the parameters 0 < q < 1 < p and λ > 0. We study the initial value problem and the global behavior of the the positive solutions. We are...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Sapienza Università Editrice
1999-01-01
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| Series: | Rendiconti di Matematica e delle Sue Applicazioni |
| Subjects: | |
| Online Access: | https://www1.mat.uniroma1.it/ricerca/rendiconti/ARCHIVIO/1999(2)/211-242.pdf |
| Summary: | In this paper, we are interested in the parabolic equation u_t − ∆u = λu^q + u^p in a bounded domain of IR^N, with the Dirichlet boundary condition and the parameters 0 < q < 1 < p and λ > 0. We study the initial value problem and the global behavior of the the positive solutions. We are mainly interested in the relations between the global (in time) solutions of the parabolic equation and the solutions of the stationary, elliptic problem. We show in particular that there exists a global solution if and only if there exists a weak solution of the stationary equation. |
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| ISSN: | 1120-7183 2532-3350 |