On the spatial blow-up and decay for some nonlinear parabolic equations with nonlinear boundary conditions |
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Authors: | R Quintanilla |
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Institution: | (1) Matemática Aplicada 2, Universidad Politècnica de Catalunya, Colón, 11 Terrassa, Barcelona, Spain |
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Abstract: | In this note we investigate the spatial behavior of several nonlinear parabolic equations with nonlinear boundary conditions.
Under suitable conditions on the nonlinear terms we prove that the solutions either cease to exist for a finite value of the
spatial variable or else they decay algebraically. The main tool used is the weighted energy method. Our results can be applied
to several situations concerning heat conduction.
Received: April 4, 2004; revised: September 20, 2004 |
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Keywords: | Parabolic equations spatial blow-up decay estimates |
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