Spectral properties of stationary solutions of the nonlinear heat equation
In this paper, we prove that if ψ is a radially symmetric, signchanging stationary solution of the nonlinear heat equation (NLH) u - ∆u = │u │ α u, in the unit ball of RN, N=3, with Dirichlet boundary conditions, then the solution of (NLH) with initial value λψ blows up infinite time if │λ - 1│....
| Authors: | , , |
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| Format: | article |
| Publication Date: | 2011 |
| Country: | España |
| Institution: | Universitat Autònoma de Barcelona |
| Repository: | Dipòsit Digital de Documents de la UAB |
| Language: | English |
| OAI Identifier: | oai:ddd.uab.cat:65204 |
| Online Access: | https://ddd.uab.cat/record/65204 https://dx.doi.org/urn:doi:10.5565/PUBLMAT_55111_09 |
| Access Level: | Open access |
| Keyword: | Semilinear heat equation Finite-time blowup Sign-changing stationary Solutions Linearized operator |
| Summary: | In this paper, we prove that if ψ is a radially symmetric, signchanging stationary solution of the nonlinear heat equation (NLH) u - ∆u = │u │ α u, in the unit ball of RN, N=3, with Dirichlet boundary conditions, then the solution of (NLH) with initial value λψ blows up infinite time if │λ - 1│. |
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