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Journal of Convex Analysis 17 (2010), No. 3&4, 827--860
Copyright Heldermann Verlag 2010

Abstract Results on the Finite Extinction Time Property: Application to a Singular Parabolic Equation

Yves Belaud
Laboratoire de Mathématiques et Physique Théorique, Faculté des Sciences et Techniques, Université François Rabelais, Parc de Grandmont, 37200 Tours, France

Jesús Ildefonso Díaz
Dep. de Matemática Aplicada, Facultad de Matemáticas, Universidad Complutense, 28040 Madrid, Spain


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
Keywords: Finite extinction time, abstract Cauchy problems, singular semilinear parabolic equations, semi-classical analysis.

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