Publication: Abstract results on the finite extinction time property: application to a singular parabolic equation
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2010-04-03
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Belaud, Yves
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Heldermann Verlag
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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.
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