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Stability of Rarefaction Waves in Viscous Media (1996)
| Content Provider | CiteSeerX |
|---|---|
| Author | Szepessy, Ers Zumbrun, Kevin |
| Abstract | : We study the time-asymptotic behavior of weak rarefaction waves of systems with strictly hyperbolic flux functions in one dimensional viscous fluids. Our main result is to show that solutions of perturbed rarefaction data converge to an approximate, "Burgers"-rarefaction wave, for initial perturbations w 0 with small mass and localized as w 0 (x) = O(jxj \Gamma1 ). The proof proceeds by iteration of a pointwise Ansatz for the error, using integral representations of its various components, based on Green's functions. We estimate the Green's functions by careful use of the Hopf-Cole transformation, combined with a refined Parametrix method. As a consequence of our method, we also obtain rates of decay and detailed pointwise estimates for the error. This pointwise method has been used successfully in studying stability of shock and constant state solutions. New features in the rarefaction case are time-varying coefficients in the linearized equations and error waves of unbounded mas... |
| File Format | |
| Volume Number | 133 |
| Journal | Arch. Rational Mech. Anal |
| Language | English |
| Publisher Date | 1996-01-01 |
| Access Restriction | Open |
| Subject Keyword | Viscous Medium Rarefaction Wave Unbounded Ma Main Result Refined Parametrix Method Integral Representation Hyperbolic Flux Function Time-asymptotic Behavior Pointwise Ansatz Rarefaction Case Detailed Pointwise Estimate Linearized Equation Perturbed Rarefaction Data Converge Initial Perturbation Proof Proceeds Time-varying Coefficient Small Mass Various Component Hopf-cole Transformation Dimensional Viscous Fluid New Feature Jxj Gamma1 Constant State Solution Weak Rarefaction Wave Error Wave Pointwise Method Careful Use Burger Rarefaction Wave |
| Content Type | Text |
| Resource Type | Article |
