Nonlinear Waves in Mechanics and Gas Dynamics
Final rept. 1 Jun 1987-30 Sep 1990
MARYLAND UNIV COLLEGE PARK DEPT OF MATHEMATICS
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The proposer has studied nonlinear hyperbolic-parabolic partial differential equations related to gas dynamics and mechanics. Hyperbolic conservation laws with relaxation are studied with applications to kinetic theory, elasticity with memory and gas flow with thermo-non-equilibrium in mind. Nonlinear waves for the compressible Navier-Stokes equations are studied for their stability and time-asymptotic behavior. The singular behavior of the magenetohydrodynamics shock waves in the small dissipation limits is clarified, in particular, it is shown that intermediate shocks are stable uniformly with regards to the strength of dissipations only for 2-dimensional model, and not for 3-dimensional model.