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Abstract results on the finite extinction time property: application to a singular parabolic equation


Díaz Díaz, Jesús Ildefonso and Belaud, Yves (2010) Abstract results on the finite extinction time property: application to a singular parabolic equation. Journal of convex analysis, 17 (3-4). pp. 827-860. ISSN 0944-6532

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We start by studying the finite extinction time for solutions of the abstract Cauchy problem u(t) + Au + Bu = 0 where A is a maximal monotone operator and B is a positive operator on a Hilbert space H. We use a suitable spectral energy method to get some sufficient conditions which guarantee this property. As application we consider a singular semilinear parabolic equation: Au = -Delta u, Bu = a(x)u(q), a(x) >= 0 bounded and -1 < q < 1, on a regular bounded domain Omega and Dirichlet boundary conditions.

Item Type:Article
Uncontrolled Keywords:Finite extinction time, abstract Cauchy problems, singular semilinear parabolic equations, semi-classical analysis. free-boundary solutions; arbitrary order; quasilinear equations; vanishing properties; elliptic problems; energy solutions; dimension; evolution; supports
Subjects:Sciences > Physics > Mathematical physics
Sciences > Mathematics > Differential equations
ID Code:15065

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