This work develops a singular perturbation theory for initial-value problems of nonlinear rst-order hyperbolic systems with stii source terms in several space variables. It is observed that under reasonable assumptions, many equations of classical physics of that type admit a structural stability condition. This condition is equivalent to the well-known… (More)
This paper is concerned with a model system for radiation hydrodynamics in multiple space dimensions. The system depends singularly on the light speed c and consists of a scalar nonlinear balance law coupled via an integral-type source term to a family of radiation transport equations. We first show existence of entropy solutions to Cauchy problems of the… (More)
In this work we propose a new numerical approach to solve some kind of degenerate parabolic equations. The underlying idea is based on the maximum principle. More precisely, we locally perturb the (initial and boundary) data instead of the nonlinear diiusion coeecients, so that the resulting problem is not degenerate. The eeciency of this method is shown… (More)
A stii system of conservation laws is analyzed with a diierence method. The existence of entropy-satisfying BV-solutions to the initial value problems is estabilished. Furthermore, we show that the solutions converge to the solutions of the corresponding equilibrium system as the relaxation time tends to zero.
This paper presents an observation that under reasonable conditions, many partial differential equations from mathematical physics possess three structural properties. One of them can be understand as a variant of the celebrated Onsager reciprocal relation in Modern Thermodynamics. It displays a direct relation of irreversible processes to the entropy… (More)
This note presents a simple approach toward interaction estimates of elementary waves for hyperbolic conservation laws. The new approach uses neither the Taylor expansion nor induction. The same technique is used to simplify the diierent interaction estimates in studying nonhomogeneous systems and initial-boundary value problems with Glimm's scheme. 1.… (More)
We derive classical particle, string and membrane motion equations from a rigorous asymptotic analysis of the Born-Infeld nonlinear electromagnetic theory. We first add to the Born-Infeld equations the corresponding energy-momentum conservation laws and write the resulting system as a non-conservative symmetric 10 × 10 system of first-order PDEs. Then, we… (More)