Accession Number : ADA332125

Title :   Nonlinear Waves in Mechanics and Gas Dynamics.

Descriptive Note : Final rept. 1 Apr 94-31 Mar 97,

Corporate Author : STANFORD UNIV CA DEPT OF MATHEMATICS

Personal Author(s) : Liu, Tai-Ping

PDF Url : ADA332125

Report Date : JUN 1997

Pagination or Media Count : 4

Abstract : The author has studied the qualitative behaviour of nonlinear waves for hyperbolic conservation laws with or without the effects of dissipations, discretization, or nonlinear resonance. The fundamental problem of well-posedness theory for hyperbolic conservation laws is being resolved. It is shown that no physical law, beyond the second law of thermodynamics, is needed. The shock waves for finite difference schemes are shown to have slow decaying tails due to the effect of small divisor. Physical degenerate dissipation matrix is shown to give rise to rich nonlinear wave phenomena. Nonlinear waves for non-strictly hyperbolic system are shown to behave sensitively as a functional of the dissipation matrix. The ideas of wave tracing and pointwise estimates introduced by the author play the central role in the analysis of these problems.

Descriptors :   *SHOCK WAVES, THERMODYNAMICS, GAS DYNAMICS, FINITE DIFFERENCE THEORY.

Subject Categories : Fluid Mechanics
      Mechanics

Distribution Statement : APPROVED FOR PUBLIC RELEASE