Abstract
We study here a model of a conservation law with a flux function with discontinuous coefficients, namely the equation $u_t + (k(x)g(u)+f(u))_x=0$. We prove the existence and the uniqueness of an entropy solution in $L^{\infty}(\mathbb R_+ \times \mathbb R)$ for $u_0$, the initial condition, in $L^{\infty}(\mathbb R)$. We provide some physical background for the study of this equation. In particular, $g$ is assumed to be neither convex nor concave and $k$ is a discontinuous function.
Citation
Florence Bachmann. "Analysis of a scalar conservation law with a flux function with discontinuous coefficients." Adv. Differential Equations 9 (11-12) 1317 - 1338, 2004. https://doi.org/10.57262/ade/1355867904
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