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Zeitschrift für Analysis und ihre Anwendungen

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Volume 31, Issue 3, 2012, pp. 307–334
DOI: 10.4171/ZAA/1462

Published online: 2012-07-11

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

Michel Pierre[1] and Julien Vovelle[2]

(1) Ecole Normale Supérieure de Rennes, Bruz, France
(2) Université Claude Bernard Lyon 1, Villeurbanne, France

We consider the Cauchy-Dirichlet problem for a nonlinear parabolic equation with $L^1$ 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.

Keywords: Parabolic equations, renormalized solution, kinetic formulation

Pierre Michel, Vovelle Julien: A Kinetic Approach in Nonlinear Parabolic Problems with $L^1$-Data. Z. Anal. Anwend. 31 (2012), 307-334. doi: 10.4171/ZAA/1462