JournalszaaVol. 31, No. 3pp. 307–334

A Kinetic Approach in Nonlinear Parabolic Problems with L1L^1-Data

  • Michel Pierre

    Ecole Normale Supérieure de Rennes, Bruz, France
  • Julien Vovelle

    Université Claude Bernard Lyon 1, Villeurbanne, France
A Kinetic Approach in Nonlinear Parabolic Problems with $L^1$-Data cover
Download PDF

Abstract

We consider the Cauchy-Dirichlet problem for a nonlinear parabolic equation with L1L^1 data. We show how the concept of kinetic formulation for conservation laws introduced by P.-L. Lions, B. Perthame and E. Tadmor [A kinetic formulation of multidimensional scalar conservation laws and related equations. J. Amer. Math. Soc. 7 (1994), 169–191]<\i> can be be used to give a new proof of the existence of renormalized solutions. To illustrate this approach, we also extend the method to the case where the equation involves an additional gradient term.

Cite this article

Michel Pierre, Julien Vovelle, A Kinetic Approach in Nonlinear Parabolic Problems with L1L^1-Data. Z. Anal. Anwend. 31 (2012), no. 3, pp. 307–334

DOI 10.4171/ZAA/1462