A NONLOCAL CONSERVATION LAW WITH NONLINEAR "RADIATION" INHOMOGENEITY

Abstract

A scalar conservation law with a nonlinear dissipative inhomogeneity, which serves as a simplified model for nonlinear heat radiation effects in high-temperature gases is studied. Global existence and uniqueness of weak entropy solutions along with L1 contraction and monotonicity properties of the solution semigroup is established. Explicit threshold conditions ensuring formation of shocks within finite time is derived. The main result proves — under further assumptions on the nonlinearity and on the initial datum — large time convergence in L1 to the self-similar N-waves of the homogeneous conservation law.