In the presence of magnetic induction and electrical fields several types of discontinuities may exist in an electrically conducting fluid. These phenomena can be described by the laws of conservation of mass, momentum, and energy; Maxwell's electromagnetic equations, and Ohm's …
Introduction Preliminaries The fractional step scheme The Riemann problem step The ODE step Estimates for the ODE step Analysis of the approximate solutions The elimination of assumptions Convergence.
We consider a system of n conservation laws: [partial derivative/boundary/degree of a polynomial symbol]∂u [over] [partial derivative/boundary/degree of a polynomial symbol]∂t + [partial derivative/boundary/degree of a polynomial symbol]∂f(u) [over] [partial derivative/boundary/…
Introduction -- Preliminaries -- Green's functions for systems with constant coefficients -- Green's function for systems linearized along shock profiles -- Estimates on green's function -- Estimates on crossing of initial layer -- Estimates on truncation error -- Energy type es…
We are interested in the time-asymptotic behavior of solutions to viscous conservation laws. Through the pointwise estimates for the Green's function of the linearized system and the analysis of coupling of nonlinear diffusion waves, we obtain explicit expressions of the time-as…
In this paper we establish the nonlinear stability of shock waves for viscous conservation laws. It is shown that when the initial data is a perturbation of viscous shock waves, then the solution converges to viscous shock waves, properly translated, as time tends to infinity.
