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Perturbation of a shock wave

Name: Perturbation of a shock wave
Creator: I. O. Rasskazov
Keywords: Perturbations in context of PDEs, line of propagation, 0101 mathematics, perturbed Hopf equation, 01 natural sciences, Asymptotic expansions of solutions to PDEs, Shocks and singularities for hyperbolic equations

descriptionPublicationkeyboard_double_arrow_right Article 01 Mar 1999Publisher:Springer Science and Business Media LLCJournal:Theoretical and Mathematical Physics, volume 118, pages 365-368 (issn: 0040-5779, eissn: 1573-9333,

Authors: I. O. Rasskazov;

doi: 10.1007/bf02557334

Perturbation of a shock wave

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Abstract

The Cauchy problem is considered for the perturbed Hopf equation \(u_t+u\), \(u_x=\varepsilon f(u)\), \(\varepsilon\to 0\). The solution in the continuity domain can be expended in the standard asymptotic series in integral powers of the small parameter. An asymptotic representation is found for the line of propagation of the shock wave.

Related Organizations

Russian Academy of Sciences
Russian Federation
Institute of Mathematics with Computer Center
Russian Federation

Keywords

Perturbations in context of PDEs, line of propagation, perturbed Hopf equation, Asymptotic expansions of solutions to PDEs, Shocks and singularities for hyperbolic equations

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