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...
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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 |
| _version_ | 1818212868975230976 |
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| author | T. Cazenave F. Dickstein M. Escobedo |
| author_facet | T. Cazenave F. Dickstein M. Escobedo |
| author_sort | T. Cazenave |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-12T05:55:14Z |
| format | Article |
| id | doaj.art-b1119ff60c594dff93b57f3fede0106b |
| institution | Directory Open Access Journal |
| issn | 1120-7183 2532-3350 |
| language | English |
| last_indexed | 2024-12-12T05:55:14Z |
| publishDate | 1999-01-01 |
| publisher | Sapienza Università Editrice |
| record_format | Article |
| series | Rendiconti di Matematica e delle Sue Applicazioni |
| spelling | doaj.art-b1119ff60c594dff93b57f3fede0106b2022-12-22T00:35:34ZengSapienza Università EditriceRendiconti di Matematica e delle Sue Applicazioni1120-71832532-33501999-01-01192211242A semilinear heat equation with concave-convex nonlinearityT. Cazenave0F. Dickstein1M. Escobedo2Université Pierre et Marie CurieUniversidade Federal do Rio de JaneiroUniversidad del País VascoIn 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.https://www1.mat.uniroma1.it/ricerca/rendiconti/ARCHIVIO/1999(2)/211-242.pdfnonlinearparabolicellipticinitial value problemglobal solutionfinite-time blow upweak solutionsupersolution |
| spellingShingle | T. Cazenave F. Dickstein M. Escobedo A semilinear heat equation with concave-convex nonlinearity Rendiconti di Matematica e delle Sue Applicazioni nonlinear parabolic elliptic initial value problem global solution finite-time blow up weak solution supersolution |
| title | A semilinear heat equation with concave-convex nonlinearity |
| title_full | A semilinear heat equation with concave-convex nonlinearity |
| title_fullStr | A semilinear heat equation with concave-convex nonlinearity |
| title_full_unstemmed | A semilinear heat equation with concave-convex nonlinearity |
| title_short | A semilinear heat equation with concave-convex nonlinearity |
| title_sort | semilinear heat equation with concave convex nonlinearity |
| topic | nonlinear parabolic elliptic initial value problem global solution finite-time blow up weak solution supersolution |
| url | https://www1.mat.uniroma1.it/ricerca/rendiconti/ARCHIVIO/1999(2)/211-242.pdf |
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