JournalsifbVol. 22, No. 2pp. 175–203

Segregation effects and gap formation in cross-diffusion models

  • Martin Burger

    Universität Erlangen-Nürnberg, Germany
  • José A. Carrillo

    University of Oxford, UK
  • Jan-Frederik Pietschmann

    Technische Universität Chemnitz, Germany
  • Markus Schmidtchen

    Imperial College London, UK
Segregation effects and gap formation in cross-diffusion models cover
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Abstract

In this paper, we extend the results of [8] by proving exponential asymptotic H1H^1-convergence of solutions to a one-dimensional singular heat equation with L2L^2-source term that describe evolution of viscous thin liquid sheets while considered in the Lagrange coordinates. Furthermore, we extend this asymptotic convergence result to the case of a time inhomogeneous source. This study has also independent interest for the porous medium equation theory.

Cite this article

Martin Burger, José A. Carrillo, Jan-Frederik Pietschmann, Markus Schmidtchen, Segregation effects and gap formation in cross-diffusion models. Interfaces Free Bound. 22 (2020), no. 2, pp. 175–203

DOI 10.4171/IFB/438