Vanishing Viscosity Solutions for Conservation Laws with Regulated Flux
| Autor: | Bressan, Alberto, Guerra, Graziano, Shen, Wen |
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| Rok vydání: | 2018 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | In this paper we introduce a concept of "regulated function" $v(t,x)$ of two variables, which reduces to the classical definition when $v$ is independent of $t$. We then consider a scalar conservation law of the form $u_t+F(v(t,x),u)_x=0$, where $F$ is smooth and $v$ is a regulated function, possibly discontinuous w.r.t.both $t$ and $x$. By adding a small viscosity, one obtains a well posed parabolic equation. As the viscous term goes to zero, the uniqueness of the vanishing viscosity limit is proved, relying on comparison estimates for solutions to the corresponding Hamilton--Jacobi equation. As an application, we obtain the existence and uniqueness of solutions for a class of $2\times2$ triangular systems of conservation laws with hyperbolic degeneracy. Comment: 36 pages, 4 figures |
| Databáze: | arXiv |
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