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|Title: ||Zero limit of dispersive-dissipative perturbed hyperbolic conservation laws|
|Authors: ||Correia, Joaquim M.C.|
|Keywords: ||Singular limit|
hyperbolic conservation law
entropy weak solution
|Issue Date: ||17-Feb-2014|
|Publisher: ||Session "Dispersive Equations and Mean-Field Models", 3rd International Conference on Dynamics, Games and Science|
|Citation: ||3rd International Conference on Dynamics, Games and Science, University of Porto, February 17–21, 2014|
|Abstract: ||We consider the initial value problem for full nonlinear dissipative-dispersive perturbations of multidimensional scalar hyperbolic conservation laws, say generalized KdV-Burgers equations.
And, as the perturbations vanish, we analyse the convergence of solutions for such problem to the classical entropy weak solution of the limit hyperbolic conservation laws.
This is a step for the proof of a “vanishing viscosity-capillarity method”. We use the setting of DiPerna’s measure-valued solution uniqueness result. The class of equations under consideration have the form of
\pa_t u+div f(u)=\eps div b(u,\grad u)+\del div \pa_(\xi) c(u,\grad u), which include generalized Korteweg-de Vries-Burgers equation (when \xi is a space variable) and Benjamin-Bona-Mahony-Burgers equation (when \xi is the time variable), or that of
\pa_t u+div f(u)=\del div c(u,\grad \pa_(\xi)u), which can present unexpected dissipative properties.|
|Appears in Collections:||CIMA - Comunicações - Em Congressos Científicos Internacionais|
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