TY - JOUR
T1 - Stability of radiative shock profiles for hyperbolic-elliptic coupled systems
AU - Nguyen, Toan
AU - Plaza, Ramón G.
AU - Zumbrun, Kevin
N1 - Funding Information:
The authors are warmly grateful to Corrado Lattanzio and Corrado Mascia for their interest in this work and for many helpful conversations, as well as their collaboration in concurrent work on the scalar case. RGP is warmly grateful to the Department of Mathematics, Indiana University, for their hospitality and financial support during two short visits in May 2008 and April 2009, when this research was carried out. The research of TN and KZ was supported in part by the National Science Foundation, award number DMS-0300487. The research of RGP was partially supported by DGAPA-UNAM through the program PAPIIT, grant IN-109008.
PY - 2010/4/15
Y1 - 2010/4/15
N2 - Extending previous work with Lattanzio and Mascia on the scalar (in fluid-dynamical variables) Hamer model for a radiative gas, we show nonlinear orbital asymptotic stability of small amplitude shock profiles of general systems of coupled hyperbolic-elliptic equations of the type modeling a radiative gas, that is, systems of conservation laws coupled with an elliptic equation for the radiation flux, including in particular the standard Euler-Poisson model for a radiating gas. The method is based on the derivation of pointwise Green function bounds and description of the linearized solution operator, with the main difficulty being the construction of the resolvent kernel in the case of an eigenvalue system of equations of degenerate type. Nonlinear stability then follows in standard fashion through linear estimates derived from these pointwise bounds, combined with energy estimates of nonlinear damping type.
AB - Extending previous work with Lattanzio and Mascia on the scalar (in fluid-dynamical variables) Hamer model for a radiative gas, we show nonlinear orbital asymptotic stability of small amplitude shock profiles of general systems of coupled hyperbolic-elliptic equations of the type modeling a radiative gas, that is, systems of conservation laws coupled with an elliptic equation for the radiation flux, including in particular the standard Euler-Poisson model for a radiating gas. The method is based on the derivation of pointwise Green function bounds and description of the linearized solution operator, with the main difficulty being the construction of the resolvent kernel in the case of an eigenvalue system of equations of degenerate type. Nonlinear stability then follows in standard fashion through linear estimates derived from these pointwise bounds, combined with energy estimates of nonlinear damping type.
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U2 - 10.1016/j.physd.2010.01.011
DO - 10.1016/j.physd.2010.01.011
M3 - Article
AN - SCOPUS:76349103020
SN - 0167-2789
VL - 239
SP - 428
EP - 453
JO - Physica D: Nonlinear Phenomena
JF - Physica D: Nonlinear Phenomena
IS - 8
ER -