We consider the Cauchy-Dirichlet problem for a nonlinear parabolic equation with 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 -Data. Z. Anal. Anwend. 31 (2012), no. 3, pp. 307–334DOI 10.4171/ZAA/1462