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 L-1 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 L-1 to the self-similar N-waves of the homogeneous conservation law.
A NON-LOCAL CONSERVATION LAW WITH NONLINEAR `RADIATION' INHOMOGENEITY
DI FRANCESCO, MARCO;
2008-01-01
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 L-1 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 L-1 to the self-similar N-waves of the homogeneous conservation law.File in questo prodotto:
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