Stability of scalar radiative shock profiles

Corrado Lattanzio, Corrado Mascia, Toa Nguyen, Ramón G. Plaza, Kevin Zumbrun

Research output: Contribution to journalArticle

11 Scopus citations

Abstract

This work establishes nonlinear orbital asymptotic stability of scalar radiative shock profiles, namely, traveling wave solutions to the simplified model system of radiating gas [K. Hamer, Quart. J. Mech. Appl. Math., 24 (1971), pp. 155-168], consisting of a scalar conservation law coupled with an elliptic equation for the radiation flux. The method is based on the derivation of pointwise Green function bounds and the description of the linearized solution operator. A new feature in the present analysis is the construction of the resolvent kernel for the case of an eigenvalue system of equations of degenerate type. Nonlinear stability then follows in standard fashion by linear estimates derived from these pointwise bounds, combined with nonlinear-damping-type energy estimates.

Original languageEnglish (US)
Pages (from-to)2165-2206
Number of pages42
JournalSIAM Journal on Mathematical Analysis
Volume41
Issue number6
DOIs
StatePublished - Dec 1 2009

All Science Journal Classification (ASJC) codes

  • Analysis
  • Computational Mathematics
  • Applied Mathematics

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    Lattanzio, C., Mascia, C., Nguyen, T., Plaza, R. G., & Zumbrun, K. (2009). Stability of scalar radiative shock profiles. SIAM Journal on Mathematical Analysis, 41(6), 2165-2206. https://doi.org/10.1137/09076026X