Abstract

We start by studying the finite extinction time for solutions of the abstract Cauchy problem ut+Au+Bu=0u_t+Au+Bu=0 where AA is a maximal monotone operator and BB is a positive operator on a Hilbert space HH. 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=−ΔuAu=-\Delta u, Bu=a(x)uqBu=a(x)u^q, a(x)≥0a(x) \geq 0 bounded and −1<q<1-1<q<1, on a regular bounded domain Ω\Omega and Dirichlet boundary conditions.

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Yves Belaud

Laboratoire de Mathématiques et Physique Théorique, Faculté des Sciences et Techniques, Université François Rabelais, Parc de Grandmont, 37200 Tours, France
and: CNRS UMR 6083

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

Keywords

  • Finite extinction time
  • abstract Cauchy problems
  • singular semilinear parabolic equations
  • semi-classical analysis

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Suggested citation

Y. Belaud, J. I. Díaz. “Abstract Results on the Finite Extinction Time Property: Application to a Singular Parabolic Equation.” Journal of Convex Analysis 17 (2010), No. 3&4, 827–860. https://doi.org/10.68381/jca17054

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