TY - JOUR
T1 - A nonlocal conservation law with nonlinear "radiation" inhomogeneity
AU - Di Francesco, M.
AU - Fellner, K.
AU - Liu, H.
PY - 2008/3/1
Y1 - 2008/3/1
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=44049096811&partnerID=8YFLogxK
UR - http://dx.doi.org/10.1142/S0219891608001465
U2 - 10.1142/S0219891608001465
DO - 10.1142/S0219891608001465
M3 - Article
AN - SCOPUS:44049096811
SN - 0219-8916
VL - 5
SP - 1
EP - 23
JO - Journal of Hyperbolic Differential Equations
JF - Journal of Hyperbolic Differential Equations
IS - 1
ER -