Evolution of the solutions of some diffusion problems with absorption (Spanish: Evolución de las soluciones de ciertos problemas de difusión con absorción)
This note is an account of results obtained by the author [Rev. Real Acad. Cienc. Exact. Fís. Natur. Madrid 75 (1981), no. 5, 1165–1183; MR0649591 (83m:35076)], and the author and J. L. Vázquez ["On a class of nonlinear parabolic equations'', to appear] about the property of compact s...
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 1980 |
| País: | España |
| Institución: | Universidad Complutense de Madrid (UCM) |
| Repositorio: | Docta Complutense |
| Idioma: | español |
| OAI Identifier: | oai:docta.ucm.es:20.500.14352/64878 |
| Acceso en línea: | https://hdl.handle.net/20.500.14352/64878 |
| Access Level: | acceso abierto |
| Palabra clave: | 517.9 Ecuaciones diferenciales 1202.07 Ecuaciones en Diferencias |
| Sumario: | This note is an account of results obtained by the author [Rev. Real Acad. Cienc. Exact. Fís. Natur. Madrid 75 (1981), no. 5, 1165–1183; MR0649591 (83m:35076)], and the author and J. L. Vázquez ["On a class of nonlinear parabolic equations'', to appear] about the property of compact support of solutions of the Cauchy problem ut=∑(∂/∂xi)(|∂u/∂xi|p−2∂u/∂xi)+α(u) in RN×(0,T), 1<p<+∞, u(0)=u0(x) in RN. The assumptions on the initial datum are u0∈L2(RN)∩L∞(RN), u0≥0, u0(x)→0 uniformly as |x|→∞, and on the absorption term α(u) they are ∫10ds/[sα(s)]1/p<∞ when p>2, and ∫10ds/α(s)<∞ when 1<p≤2. It is shown, by means of comparison with suitable supersolutions, that for t>0 the support of x↦u(t,x) is compact (even if the initial datum is not compactly supported) and that the solution disappears in finite time, i.e., u(x,t)≡0 if t>t0, where t0 is a positive number depending upon u0. |
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