A nonlocal conservation law with nonlinear "radiation" inhomogeneity

M. Di Francesco, K. Fellner, H. Liu

Research output: Contribution to journalArticle

6 Citations (Scopus)

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 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 to the self-similar N-waves of the homogeneous conservation law.
Original languageEnglish
Pages (from-to)1-23
Number of pages23
JournalJournal of Hyperbolic Differential Equations
Volume5
Issue number1
DOIs
Publication statusPublished - 1 Mar 2008

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