Systems of conservation laws

Hyperbolic Systems of Conservation Laws

Its purpose is to provide an account of some recent advances in the mathematical theory of hyperbolic systems of conservation laws in one space dimension. After a brief review of basic concepts, we describe in detail the method of wave-front tracking approximation and present some of the latest results on uniqueness and stability of entropy weak solutions. 1-Review of basic theory. This chapter...

Hyperbolic Systems of Conservation Laws

Conservation laws are first order systems of quasilinear partial differential equations in divergence form; they express the balance laws of continuum physics for media with "elastic" response, in which internal dissipation is neglected. The absence of internal dissipation is manifested in the emergence of solutions with jump discontinuities across manifolds of codimension one, representing, in...

Stability of systems of viscous conservation laws

Systems of Hyperbolic Conservation Laws with Memory

Global weak solutions of bounded variation to systems of balance laws with non-local source are constructed by the method of vanishing viscosity. Suitable dissipativeness assumptions are imposed on the source terms to assure convergence of the method. Under these hypotheses, the total variation remains uniformly bounded and integrable in time, the vanishing viscosity solutions are uniformly sta...

Invariant Regions for Systems of Conservation Laws

We describe necessary and sufficient conditions for a region in R." to be invariant for (Glimm) solutions of the system of n conservation laws Ut + f(u)x = 0. We also make some observations about the invariance of such regions for certain finite difference approximations of solutions of systems of conservation laws.