Pré-Publication, Document De Travail Année : 2006

Analysis of a Scalar Conservation Law with Space Discontinuous Advection Function in a Bounded Domain

Résumé

We deal with the scalar conservation law in a one dimensional bounded domain : $\Omega: \partial_t u + \partial_x(k(x)g(u)) = 0$, associated with a bounded initial value $u_0$. The function $k$ is supposed to be bounded, discontinuous at ${x_0 = 0}$, and with bounded variation. A weak entropy formulation for the Cauchy problem has been introduced by J.D Towers in [11]. In [10] the existence and the uniqueness is proved by N. Seguin and J. Vovelle through a regularization of the function $k$. We generalize the definition of J.D Towers and we adapt the method developed in [10] to establish an existence and uniqueness property in the case of the homogeneous Dirichlet boundary conditions.

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hal-00220437 , version 1 (28-01-2008)

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  • HAL Id : hal-00220437 , version 1

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Julien Jimenez, Laurent Levi, Monique Madaune-Tort. Analysis of a Scalar Conservation Law with Space Discontinuous Advection Function in a Bounded Domain. 2006. ⟨hal-00220437⟩
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