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On the spatial blow-up and decay for some nonlinear parabolic equations with nonlinear boundary conditions

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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.

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  1. Matemática Aplicada 2, Universidad Politècnica de Catalunya, Colón, 11 Terrassa, Barcelona, Spain

    R. Quintanilla

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  1. R. Quintanilla
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Correspondence to R. Quintanilla.

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Received: April 4, 2004; revised: September 20, 2004

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Quintanilla, R. On the spatial blow-up and decay for some nonlinear parabolic equations with nonlinear boundary conditions. Z. angew. Math. Phys. 57, 595–603 (2006). https://doi.org/10.1007/s00033-005-0035-4

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  • DOI: https://doi.org/10.1007/s00033-005-0035-4

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