Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4614633 | Journal of Mathematical Analysis and Applications | 2016 | 25 Pages |
Abstract
The paper considers a scalar conservation law with a discontinuous flux F of the form F(x,u)=H(x)g(u)+(1âH(x))h(u) where H(x) is the Heaviside function. Herein, the fluxes g and h are supposed to have one minimum and no maximum and at most one crossing in the interior of the domain of definition. The aim is to verify a weak solution of such a problem in the following way: We are looking for discrete shock profiles for its continuously differentiable perturbation with a parameter ε and Godunov's scheme for conservation laws with spatially varying flux functions. The obtained discrete shock profile satisfies a discrete entropy condition of Kruzkhov type and after letting εâ0, approaches an entropy weak solution of the original equation.
Keywords
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Physical Sciences and Engineering
Mathematics
Analysis
Authors
Tanja KruniÄ, Marko Nedeljkov,