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Monotonicity of solutions and blow-up for semilinear parabolic equations with nonlinear memory

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Abstract

We show the existence of monotone in time solutions for a semilinear parabolic equation with memory. The blow-up rate estimate of the solution is known to be a consequence of the monotonicity property.

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Authors and Affiliations

  1. Département de Mathématiques, Université de Picardie, INSSET, 02109, St-Quentin, France

    Philippe Souplet

  2. Laboratoire de Mathématiques Appliquées, UMR CNRS 7641, Université de Versailles, 78035, 45 avenue des Etats-Unis, Versailles, France

    Philippe Souplet

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  1. Philippe Souplet
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Correspondence to Philippe Souplet.

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Souplet, P. Monotonicity of solutions and blow-up for semilinear parabolic equations with nonlinear memory . Z. angew. Math. Phys. 55, 28–31 (2004). https://doi.org/10.1007/s00033-003-1158-0

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  • DOI: https://doi.org/10.1007/s00033-003-1158-0

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