Compactness for nonlinear continuity equations

Pierre-Emmanuel Jabin 1, 2 Fethi Ben Belgacem 3, 4
1 TOSCA
INRIA Lorraine, CRISAM - Inria Sophia Antipolis - Méditerranée , UHP - Université Henri Poincaré - Nancy 1, Université Nancy 2, INPL - Institut National Polytechnique de Lorraine, CNRS - Centre National de la Recherche Scientifique : UMR7502
Abstract : We prove compactness and hence existence for solutions to a class of non linear transport equations. The corresponding models combine the features of linear transport equations and scalar conservation laws. We introduce a new method which gives quantitative compactness estimates compatible with both frameworks.
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Pierre-Emmanuel Jabin, Fethi Ben Belgacem. Compactness for nonlinear continuity equations. [Research Report] 2011. ⟨hal-00719462⟩

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