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Evolution of the solutions of some diffusion problems with absorption (Spanish: Evolución de las soluciones de ciertos problemas de difusión con absorción)

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Herrero, Miguel A. (1980) Evolution of the solutions of some diffusion problems with absorption (Spanish: Evolución de las soluciones de ciertos problemas de difusión con absorción). Publicacions de la Secció de Matemàtiques. Universitat Autònoma de Barcelona, 19 (1). pp. 117-130. ISSN 0210-2978

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Official URL: http://mat.uab.cat/pubmat/articles/view_doi/10.5565/PUBLMAT_19180_09


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Abstract

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.


Item Type:Article
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Proceedings of the second conference on differential equations and their applications, II (Valldoreix, 1979)

Subjects:Sciences > Mathematics > Differential equations
ID Code:22801
Deposited On:13 Sep 2013 16:08
Last Modified:19 Feb 2019 11:26

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