Dafermos regularization of a diffusive-dispersive equation with cubic flux
نویسندگان
چکیده
منابع مشابه
Dafermos Regularization of a Diffusive-dispersive Equation with Cubic Flux
We study existence and spectral stability of stationary solutions of the Dafermos regularization of a much-studied diffusive-dispersive equation with cubic flux. Our study includes stationary solutions that corresponds to Riemann solutions consisting of an undercompressive shock wave followed by a compressive shock wave. We use geometric singular perturbation theory (1) to construct the solutio...
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For a system of conservation laws in one space dimension, we identify all structurally stable Riemann solutions that include only shock waves. Shock waves are required to satisfy the viscous profile criterion for a given viscosity (B(u)ux)x . Undercompressive shock waves are allowed. We also show that all such Riemann solutions have nearby smooth solutions of the Dafermos regularization with th...
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The result of this paper is that certain composite-wave solutions of scalar conservation laws have nearby scale-invariant solutions of the Dafermos regularization. This result supports the conjecture that all structurally stable Riemann solutions have scale-invariant solutions of the Dafermos regularization nearby. It thereby supports the validity of approximating Riemann solutions by numerical...
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We consider two physically and mathematically distinct regularization mechanisms of scalar hyperbolic conservation laws. When the flux is convex, the combination of di↵usion and dispersion are known to give rise to monotonic and oscillatory traveling waves that approximate shock waves. The zero-di↵usion limits of these traveling waves are dynamically expanding dispersive shock waves (DSWs). A r...
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For the case B(u) ≡ I and a Riemann solution consisting of n Lax shocks, I shall explain how geometric singular perturbation theory can be used to construct the u2(x) and to find eigenvalues and eigenfunctions of the linearization of (4) at u2(x). The eigenvalues are related to (i) eigenvalues of the traveling waves that correspond to the individual shock waves, which have been studied by a num...
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ژورنال
عنوان ژورنال: Discrete and Continuous Dynamical Systems
سال: 2012
ISSN: 1078-0947
DOI: 10.3934/dcds.2012.32.4069