Entropy solutions for weakly coupled hyperbolic systems in several space dimensions

Abstract.

Systems of nonlinear hyperbolic conservation laws in several space dimensions are considered which are characterized by the fact that the coupling of the equations is only due to source terms. These weakly coupled systems arise in a variety of applications like hydrological problems, the theory of reactive flows, relaxation schemes, or mathematical biology. We present an existence and uniqueness theorem for certain entropy solutions of a general class of weakly coupled hyperbolic initial value problems. The approach relies on the analysis of the associated parabolically regularized Cauchy problem.¶The result for the general problem is applied tophysically relevant examples. Existence and uniquenessof entropy solutions for problems from combustion theory,hydrology and other areas is verified.