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Weak solutions and supersolutions in L 1 for reaction-diffusion systems

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Nonlinear Evolution Equations and Related Topics

Abstract

We prove here that limits of nonnegative solutions to reaction-diffusion systems whose nonlinearities are bounded in L 1 always converge to supersolutions of the system. The motivation comes from the question of global existence in time of solutions for the wide class of systems preserving positivity and for which the total mass of the solution is uniformly bounded. We prove that, for a large subclass of these systems, weak solutions exist globally.

A Philippe, mon maître et ami

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Authors and Affiliations

  1. Antenne de Bretagne de l’ENS Cachan et Institut de Recherche Mathématique de Rennes, Campus de Ker Lann, Bruz, 35170, France

    Michel Pierre

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  1. Michel Pierre
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Editor information

Editors and Affiliations

  1. Department of Applied Analysis, University of Ulm, 89069, Ulm, Germany

    Wolfgang Arendt

  2. Analyse Numérique, Université Pierre et Marie Curie, B.C. 187, 4, place Jussieu, 75252, Paris Cedex 05, France

    Haïm Brézis

  3. Department of Mathematics Hill Center, Busch Campus, Rutgers University, 110 Frelinghuysen RD, Piscataway, NJ, 08854, USA

    Haïm Brézis

  4. Campus de Ker Lann, Antenne de Bretagne de l’ENS Cachan, 35170, Bruz, France

    Michel Pierre

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© 2003 Springer Basel AG

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Pierre, M. (2003). Weak solutions and supersolutions in L 1 for reaction-diffusion systems. In: Arendt, W., Brézis, H., Pierre, M. (eds) Nonlinear Evolution Equations and Related Topics. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-7924-8_8

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  • DOI: https://doi.org/10.1007/978-3-0348-7924-8_8

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-7643-7107-4

  • Online ISBN: 978-3-0348-7924-8

  • eBook Packages: Springer Book Archive

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