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Shock Waves in Conservation Laws with Physical Viscosity (Memoirs of the American Mathematical Society)

Differential Equations

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About the Author Tai-Ping Liu, Institute of Mathematics, Academia Sinica, Taipei, Taiwan, and Stanford University, CA, USA.Yanni Zeng, University of Alabama at Birmingham, AL, USA. Product Description The authors study the perturbation of a shock wave in conservation laws with physical viscosity. They obtain the detailed pointwise estimates of the solutions. In particular, they show that the solution converges to a translated shock profile. The strength of the perturbation and that of the shock are assumed to be small but independent. The authors' assumptions on the viscosity matrix are general so that their results apply to the Navier-Stokes equations for the compressible fluid and the full system of magnetohydrodynamics, including the cases of multiple eigenvalues in the transversal fields, as long as the shock is classical. The authors' analysis depends on accurate construction of an approximate Green's function. The form of the ansatz for the perturbation is carefully constructed and is sufficiently tight so that the author can close the nonlinear term through Duhamel's principle.

Product Specifications

Format: Paperback
ASIN: 1470410168
Category: Books > Subjects > Science, Nature & Maths > Mathematics > Mathematical Analysis > Differential Equations
Domain: Amazon UK
Release Date: 30 March 2015
Listed Since: 05 December 2014

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Shock Waves in Conservation Laws with Physical Viscosity (Memoirs of the American Mathematical Society)

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