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