Stability of scalar radiative shock prof
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Stability of scalar radiative shock prof
arXiv:0905.4448vl [math. A P] 27 May 2009STABILITY OF SCALAR RADIATIVE SHOCK PROFILES'CORRADO LATTANZIO*. CORRADO MASCIA*. TO AN NGUYENS. RAMÓN G. pla Stability of scalar radiative shock profaza’, AND KEVIN ZUMBRUN5Abstract. This work establishes nonlinear orbital asymptotic stability of scalar radiative shock profiles, namely, traveling wave solutions to the simplified model system of radiating gas [8], consisting of a scalar cxMiscrvalion law coupled with an elliptic equation for the* Stability of scalar radiative shock prof radiation flux. The method is based on the derivation of pointwise Green function bounds and description of the linearized solution operator. A new fStability of scalar radiative shock prof
eature in the present analysis Is the construction of the resolvent kernel for the case of an eigenvalue system of equations of degenerate type. NonliarXiv:0905.4448vl [math. A P] 27 May 2009STABILITY OF SCALAR RADIATIVE SHOCK PROFILES'CORRADO LATTANZIO*. CORRADO MASCIA*. TO AN NGUYENS. RAMÓN G. pla Stability of scalar radiative shock profestimates.Key words. Hyperbolic-elliptic coupled systems. Radiative shock, pointwise Green function bounds, Evans function.AMS subject classifications. 35IÌ35 (34B27 35M20 7G.N15)1. Introduction, rhe one-dimensional motion of a radiating gas (due to high-temperature effects) can be modeled by the co Stability of scalar radiative shock profmpressible Euler equations coupled with an elliptic equation for the radiative flux term [8. 39]. The present work considers the following simplifiedStability of scalar radiative shock prof
model system of a radiating gastit + X(u)» +0-Stability of scalar radiative shock prof
ay refer to [17, 19. 8Ì-Formally, one may express q in terms of u as q = — KM(u)r, where K = (1 — so I hill system (1.1 Ị rejmwenrs some regularizatioarXiv:0905.4448vl [math. A P] 27 May 2009STABILITY OF SCALAR RADIATIVE SHOCK PROFILES'CORRADO LATTANZIO*. CORRADO MASCIA*. TO AN NGUYENS. RAMÓN G. pla Stability of scalar radiative shock profrk was supported in port by the National Science Foundation award number DMS-0300487. CL. CM and RGP are warmly grateful to the Department of Mathematics, Indiana University. for their hospitality and financial support during two short visits in May 2008 and April 2tM», when this research was carrie Stability of scalar radiative shock profd out. The research of RGP was partially supported by DGAPA-UNAM through the program PAPUT, grant IN-109008.tDIpartlmcnto di Matcinatlca Pure cd ApphcStability of scalar radiative shock prof
ata, Unlvccsiti doll’Aquila, via Votolo, Coppito, 1-G7010 L’Aquila (Italy):Dipartiincnto di Matcmaticn “G. Castelnuoro". Sapicnza, Università di Roma,arXiv:0905.4448vl [math. A P] 27 May 2009STABILITY OF SCALAR RADIATIVE SHOCK PROFILES'CORRADO LATTANZIO*. CORRADO MASCIA*. TO AN NGUYENS. RAMÓN G. pla Stability of scalar radiative shock profánica, 1IMAS-UNAM. Apdo. Postal 20-720. c.p. 01000 Mexico D.F. (Mẻxtoo)https://khothuvien.cori!2 C.LATTANZIO. C.MASCIA. T.NGUYEN. R.G.PLAZA AND K.ZVMBRUNfor all a under consideration, conveying the right sign in the diffusion coming from Chapman Enskog expansion (see |36|).We are interested in trave Stability of scalar radiative shock profling wave solutions to system (1.1) of the form(«.ợ)(xự.)(b\Q)(x st), (UQ)(±oc)(u±.O),(1.3)where the triple (u+.u_,s) is a shock front of Lax type ofStability of scalar radiative shock prof
the underlying scalar conservation law for the velocity,M. + /(«)x=0,(1-4)satisfying Rankine Hngoniot condition /(u I ) — /(« ) = x(tx I — n ), and TaarXiv:0905.4448vl [math. A P] 27 May 2009STABILITY OF SCALAR RADIATIVE SHOCK PROFILES'CORRADO LATTANZIO*. CORRADO MASCIA*. TO AN NGUYENS. RAMÓN G. pla Stability of scalar radiative shock profictly convex.J?W>0(1.5)for all M under consideration, for which the entropy condition reduces to It I < tx . We refer to Wfflf' solutions of the form (1.3) to the system (I. I), under the Lax shock assumption for the scalar conservation law, as radiative shock profiles. The existence and regularity Stability of scalar radiative shock profof traveling waves of this type under hypotheses (1.2) is known 16. 22]. even for non-convex velocity fluxes |22|.According to custom and without lossStability of scalar radiative shock prof
of generality, we can reduce to the case of a stationary profile s = 0, by int roducing a convenient change of variable and relal>eling the flux funcarXiv:0905.4448vl [math. A P] 27 May 2009STABILITY OF SCALAR RADIATIVE SHOCK PROFILES'CORRADO LATTANZIO*. CORRADO MASCIA*. TO AN NGUYENS. RAMÓN G. pla Stability of scalar radiative shock prof-Ọ" + Q + M(uy = 0.1(here ’ denotes differentiation with respect to x), connecting endpoints (t<±,0) at ±oc, that is,lint (U.Q)(x) = (u±.O).Therefore, we summarize our main structural assumptions as follows:/, A/ €(regularity),(A0)&.»•■(genuine nonlinearity),(Al)/(«)=/(«,),(Rankine Hugoniot conditio Stability of scalar radiative shock profn).(A2)u+ < u_,(Lax entropy condition),(A3), dM(positive diffusion).(A4)arXiv:0905.4448vl [math. A P] 27 May 2009STABILITY OF SCALAR RADIATIVE SHOCK PROFILES'CORRADO LATTANZIO*. CORRADO MASCIA*. TO AN NGUYENS. RAMÓN G. plaarXiv:0905.4448vl [math. A P] 27 May 2009STABILITY OF SCALAR RADIATIVE SHOCK PROFILES'CORRADO LATTANZIO*. CORRADO MASCIA*. TO AN NGUYENS. RAMÓN G. plaGọi ngay
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