On unified theory for scalar conservation laws with fluxes and sources discontinuous with respect to the unknown
| Autor: | Bulíček, Miroslav, Gwiazda, Piotr, Świerczewska-Gwiazda, Agnieszka |
|---|---|
| Rok vydání: | 2016 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | We deal with the Cauchy problem for multi-dimensional scalar conservation laws, where the fluxes and the source terms can be discontinuous functions of the unknown. The main novelty of the paper is the introduction of a~kinetic formulation for the considered problem. To handle the discontinuities we work in the framework of re-parametrization of the flux and the source functions, which was previously used for Kru\v{z}kov entropy solutions. Within this approach we obtain a fairly complete picture: existence of entropy measure valued solutions, entropy weak solutions and their equivalence to the kinetic solution. The results of existence and uniqueness follow under the assumption of H\"{o}lder continuity at zero of the flux. The source term, what is another novelty for the studies on problems with discontinuous flux, is only assumed to be one-side Lipschitz, not necessarily monotone function. Comment: 42 pages |
| Databáze: | arXiv |
| Externí odkaz: |
|