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# An Engquist-Osher-Type Scheme for Conservation Laws with Discontinuous Flux Adapted to Flux Connections

@article{Brger2009AnES, title={An Engquist-Osher-Type Scheme for Conservation Laws with Discontinuous Flux Adapted to Flux Connections}, author={Raimund B{\"u}rger and Kenneth H. Karlsen and John D. Towers}, journal={SIAM J. Numerical Analysis}, year={2009}, volume={47}, pages={1684-1712} }

- Published 2009 in SIAM J. Numerical Analysis
DOI:10.1137/07069314X

We consider scalar conservation laws with the spatially varying flux H(x)f(u)+(1−H(x))g(u), where H(x) is the Heaviside function and f and g are smooth nonlinear functions. Adimurthi, Mishra, and Veerappa Gowda [J. Hyperbolic Differ. Equ. 2:783–837, 2005] pointed out that such a conservation law admits many L1 contraction semigroups, one for each so-called connection (A, B). Here we define entropy solutions of type (A, B) involving Kružkov-type entropy inequalities that can be adapted to any… CONTINUE READING

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