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
belaud@lmpt.univ-tours.fr
Jesús Ildefonso Díaz
Dep. de Matemática Aplicada, Facultad de Matemáticas, Universidad Complutense, 28040 Madrid, Spain
ji_diaz@mat.ucm.es
[Abstract-pdf]
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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