On reflection of shock front in multidimensional space
Chen Shuxing (1987-1988)
Séminaire Équations aux dérivées partielles (Polytechnique)
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Chen Shuxing (1987-1988)
Séminaire Équations aux dérivées partielles (Polytechnique)
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Yu. G. Rykov (2002)
Bollettino dell'Unione Matematica Italiana
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The paper deals with the 2-D system of gas dynamics without pressure which was introduced in 1970 by Ua. Zeldovich to describe the formation of largescale structure of the Universe. Such system occurs to be an intermediate object between the systems of ordinary differential equations and hyperbolic systems of PDE. The main its feature is the arising of singularities: discontinuities for velocity and d-functions of various types for density. The rigorous notion of generalized solutions...
Rinaldo M. Colombo (2004)
Applications of Mathematics
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This paper contains several recent results about nonlinear systems of hyperbolic conservation laws obtained through the technique of Wave Front Tracking.
Abbassi, Adil, Namah, Gawtum (2005)
Mathematical Problems in Engineering
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Jeffrey Rauch, Chunjing Xie, Zhouping Xin (2011-2012)
Séminaire Laurent Schwartz — EDP et applications
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We prove global dynamical stability of steady transonic shock solutions in divergent quasi-one-dimensional nozzles. One of the key improvements compared with previous results is that we assume neither the smallness of the slope of the nozzle nor the weakness of the shock strength. A key ingredient of the proof are the derivation a exponentially decaying energy estimates for a linearized problem.