Niveau: Supérieur, Doctorat, Bac+8
One-dimensional transport equations with discontinuous coefficients Franc¸ois Bouchut? Franc¸ois James† November 24, 2009 Abstract We consider one-dimensional linear transport equations with bounded but possibly discontinuous coefficient a. The Cauchy problem is studied from two different points of view. In the first case we assume that a is piecewise continuous. We give an existence result and a precise description of the solutions on the lines of discontinuity. In the second case, we assume that a satisfies a one-sided Lipschitz condition. We give existence, uniqueness and general stability results for backward Lipschitz solutions and forward measure solutions, by using a duality method. We prove that the flux associated to these measure solutions is a product by some canonical representative a? of a. Key-words. Linear transport equations, discontinuous coefficients, weak stability, duality, product of a measure by a discontinuous function, nonnegative solutions. 1991 Mathematics Subject Classification. Primary 35F10, 35B35, 34A12. To appear in Nonlinear Analysis, TMA ?Departement de Mathematiques et Applications, UMR CNRS 8553, Ecole Normale Superieure et CNRS, 45 rue d'Ulm, 75230 Paris Cedex 05, France, †Mathematiques, Applications et Physique Mathematique d'Orleans, UMR CNRS 6628, Universite d'Orleans, 45067 Orleans Cedex 2, France, .
- unique reversible backward
- product a∂xu
- problem
- reversible solutions
- linear problems
- transport equations
- condition holds
- canonical representative a?
- homogeneous linear