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Stable boundary layers in a diffusion problem with nonlinear reaction at the boundary

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Abstract

We prove the existence of nonconstant stable stationary solutions of an evolution problem with a nonlinear reaction acting on the boundary. These solutions present layers at certain points of the boundary. We also study the behavior of these solutions as the small parameter appearing in the equation approaches zero and show some stability properties of the profiles given by these equilibrium solutions.

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Authors and Affiliations

  1. Departamento de Matemática Aplicada Universidad Complutense de Madrid, 28040, Madrid, Spain

    José M. Arrieta & Anibal Rodríguez-Bernal

  2. Departament de Matemática Aplicada I, Universitat Politècnica de Catalunya, 08028, Barcelona, Spain

    Neus Cónsul

Authors
  1. José M. Arrieta
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  2. Neus Cónsul
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  3. Anibal Rodríguez-Bernal
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Correspondence to José M. Arrieta.

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Arrieta, J., Cónsul, N. & Rodríguez-Bernal, A. Stable boundary layers in a diffusion problem with nonlinear reaction at the boundary . Z. angew. Math. Phys. 55, 1–14 (2004). https://doi.org/10.1007/s00033-003-2063-z

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  • DOI: https://doi.org/10.1007/s00033-003-2063-z

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