A kinetic approach in nonlinear parabolic problems with L1-data.

Michel Pierre (1) , Julien Vovelle (2)

1 IRMAR - Institut de Recherche Mathématique de Rennes
2 ICJ - Institut Camille Jordan

We consider the Cauchy-Dirichlet problem for a nonlinear parabolic equation with L1 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.

Mots clés: Parabolic equations; renormalized solution; kinetic formulation

Domaines: Equations aux dérivées partielles [math.AP]

Michel Pierre, Julien Vovelle. A kinetic approach in nonlinear parabolic problems with L1-data.. Zeitschrift für Analysis und ihre Anwendungen, 2012, 31 (3), pp.307-334. ⟨10.4171/ZAA/1462⟩. ⟨hal-00776461⟩