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

Abstract : 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.
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https://hal.archives-ouvertes.fr/hal-00776461
Contributor : Marie-Annick Guillemer Connect in order to contact the contributor
Submitted on : Tuesday, January 15, 2013 - 3:43:38 PM
Last modification on : Tuesday, October 19, 2021 - 10:48:08 AM

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

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