A nonlocal conservation law with nonlinear "radiation" inhomogeneity
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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.
|Creators||Di Francesco, M., Fellner, K. and Liu, H.|
|Departments||Faculty of Science > Mathematical Sciences|
Faculty of Engineering & Design > Electronic & Electrical Engineering
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