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

作者：Pierre Michel^*; Vovelle Julien

来源：Zeitschrift fur Analysis und Ihre Anwendungen, 2012, 31(3): 307-334.

DOI：10.4171/ZAA/1462

• Parabolic equations
• renormalized solution
• kinetic formulation

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] 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.

• 出版日期2012