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Book Synopsis
This monograph examines multidimensional stability of strong discontinuities (e.g. shock waves) for systems of conservation laws and surveys the author''s results for models of ideal magnetohydrodynamics (classical, ''pressure anisotropic'', relativistic) and electrohydrodynamics. The primary attention is concentrated on linearised stability analysis, especially on the issue of uniform stability in the sense of the uniform Kreiss-Lopatinski condition. A so-called ''equational'' approach based on obtaining, by the dissipative integrals technique, a priori estimates without loss of smoothness for corresponding linearised stability problems in the domains of uniform stability is described. Recent results for ideal models of MHD (classical MHD, ''pressure anisotropic'' MHD of Chew, Goldberger and Low, relativistic MHD) and also for a certain non-hyperbolic model are presented as the system of electrohydrodynamics (EHD).

Stability of Strong Discontinuities in

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    A Hardback by Alexander Blokhin, Yuri Trakhinin

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      Publisher: Nova Science Publishers Inc
      Publication Date: Publication Date: 22/12/2003
      ISBN13: 9781590337523, 978-1590337523
      ISBN10: 1590337522

      Description

      Book Synopsis
      This monograph examines multidimensional stability of strong discontinuities (e.g. shock waves) for systems of conservation laws and surveys the author''s results for models of ideal magnetohydrodynamics (classical, ''pressure anisotropic'', relativistic) and electrohydrodynamics. The primary attention is concentrated on linearised stability analysis, especially on the issue of uniform stability in the sense of the uniform Kreiss-Lopatinski condition. A so-called ''equational'' approach based on obtaining, by the dissipative integrals technique, a priori estimates without loss of smoothness for corresponding linearised stability problems in the domains of uniform stability is described. Recent results for ideal models of MHD (classical MHD, ''pressure anisotropic'' MHD of Chew, Goldberger and Low, relativistic MHD) and also for a certain non-hyperbolic model are presented as the system of electrohydrodynamics (EHD).

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