Stability of scalar radiative shock profiles

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

Research output: Contribution to journalArticle

11 Citations (Scopus)

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

Fingerprint

Asymptotic stability
Green's function
Shock
Conservation
Damping
Scalar
Fluxes
Orbital Stability
Radiation
Nonlinear Damping
Scalar Conservation Laws
Energy Estimates
Nonlinear Stability
Traveling Wave Solutions
Resolvent
Gases
Asymptotic Stability
Elliptic Equations
System of equations
kernel

All Science Journal Classification (ASJC) codes

  • Analysis
  • Computational Mathematics
  • Applied Mathematics

Cite this

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
Lattanzio, Corrado ; Mascia, Corrado ; Nguyen, Toan ; Plaza, Ramón G. ; Zumbrun, Kevin. / Stability of scalar radiative shock profiles. In: SIAM Journal on Mathematical Analysis. 2009 ; Vol. 41, No. 6. pp. 2165-2206.
@article{d1754da046b44d3b97d4dc8fc2b73cc3,
title = "Stability of scalar radiative shock profiles",
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.",
author = "Corrado Lattanzio and Corrado Mascia and Toan Nguyen and Plaza, {Ram{\'o}n G.} and Kevin Zumbrun",
year = "2009",
month = "12",
day = "1",
doi = "10.1137/09076026X",
language = "English (US)",
volume = "41",
pages = "2165--2206",
journal = "SIAM Journal on Mathematical Analysis",
issn = "0036-1410",
publisher = "Society for Industrial and Applied Mathematics Publications",
number = "6",

}

Lattanzio, C, Mascia, C, Nguyen, T, Plaza, RG & Zumbrun, K 2009, 'Stability of scalar radiative shock profiles', SIAM Journal on Mathematical Analysis, vol. 41, no. 6, pp. 2165-2206. https://doi.org/10.1137/09076026X

Stability of scalar radiative shock profiles. / Lattanzio, Corrado; Mascia, Corrado; Nguyen, Toan; Plaza, Ramón G.; Zumbrun, Kevin.

In: SIAM Journal on Mathematical Analysis, Vol. 41, No. 6, 01.12.2009, p. 2165-2206.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Stability of scalar radiative shock profiles

AU - Lattanzio, Corrado

AU - Mascia, Corrado

AU - Nguyen, Toan

AU - Plaza, Ramón G.

AU - Zumbrun, Kevin

PY - 2009/12/1

Y1 - 2009/12/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=76349105984&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=76349105984&partnerID=8YFLogxK

U2 - 10.1137/09076026X

DO - 10.1137/09076026X

M3 - Article

VL - 41

SP - 2165

EP - 2206

JO - SIAM Journal on Mathematical Analysis

JF - SIAM Journal on Mathematical Analysis

SN - 0036-1410

IS - 6

ER -