Please use this identifier to cite or link to this item: http://hdl.handle.net/10174/13667

 Title: Zero limit of dispersive-dissipative perturbed hyperbolic conservation laws Authors: Correia, Joaquim M.C. Keywords: Singular limitdissipationviscositydispersioncapilllarityBurgers equationKdV-type equationhyperbolic conservation lawshock waveentropy weak solutionmeasure-valued 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. URI: http://www.fc.up.pt/dgsiii/programme.htmlhttp://hdl.handle.net/10174/13667 Type: lecture Appears in Collections: CIMA - Comunicações - Em Congressos Científicos Internacionais

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