Geodesic
Abstract Results on the Finite Extinction Time Property: Application to a Singular Parabolic Equation
Journal of convex analysis, Tome 17 (2010) no. 3, pp. 827-86.

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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: $Au=-\Delta u$, $Bu=a(x)u^q$, $a(x) \geq 0$ bounded and $-1$, on a regular bounded domain $\Omega$ and Dirichlet boundary conditions.
Mots-clés : Finite extinction time, abstract Cauchy problems, singular semilinear parabolic equations, semi-classical analysis 
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     author = {Y. Belaud and J. I. D{\'\i}az},
     title = {Abstract {Results} on the {Finite} {Extinction} {Time} {Property:} {Application} to a {Singular} {Parabolic} {Equation}},
     journal = {Journal of convex analysis},
     pages = {827--86},
     publisher = {mathdoc},
     volume = {17},
     number = {3},
     year = {2010},
     url = {http://geodesic.mathdoc.fr/item/JCA_2010_17_3_JCA_2010_17_3_a8/}
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Y. Belaud; J. I. Díaz. Abstract Results on the Finite Extinction Time Property: Application to a Singular Parabolic Equation. Journal of convex analysis, Tome 17 (2010) no. 3, pp. 827-86. http://geodesic.mathdoc.fr/item/JCA_2010_17_3_JCA_2010_17_3_a8/