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Convergence to Separate Variables Solutions for a Degenerate Parabolic Equation with Gradient Source

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Abstract

The large time behaviour of nonnegative solutions to a quasilinear degenerate diffusion equation with a source term depending solely on the gradient is investigated. After a suitable rescaling of time, convergence to a unique profile is shown for global solutions. The proof relies on the half-relaxed limits technique within the theory of viscosity solutions and on the construction of suitable supersolutions and barrier functions to obtain optimal temporal decay rates and boundary estimates. Blowup of weak solutions is also studied.

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Authors and Affiliations

  1. Institut de Mathématiques de Toulouse, CNRS UMR 5219, Université de Toulouse, 31062, Toulouse Cedex 9, France

    Philippe Laurençot

  2. Fakultät für Mathematik, Universität Duisburg-Essen, 45117, Essen, Germany

    Christian Stinner

Authors
  1. Philippe Laurençot
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  2. Christian Stinner
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Correspondence to Christian Stinner.

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Laurençot, P., Stinner, C. Convergence to Separate Variables Solutions for a Degenerate Parabolic Equation with Gradient Source. J Dyn Diff Equat 24, 29–49 (2012). https://doi.org/10.1007/s10884-011-9238-x

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  • DOI: https://doi.org/10.1007/s10884-011-9238-x

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