Geometric optics with critical vanishing viscosity for one-dimensional semilinear initial value problems

Stéphane
 
Junca

doi:rmi/1218475353

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July, 2008 Geometric optics with critical vanishing viscosity for one-dimensional semilinear initial value problems

Stéphane Junca

Rev. Mat. Iberoamericana 24(2): 549-566 (July, 2008).

Abstract

We study the propagation of high frequency oscillations for one dimensional semi-linear hyperbolic systems with small parabolic perturbations. We obtain a new degenerate parabolic system for the profile, and valid an asymptotic development in the spirit of Joly, Métivier and Rauch.

Citation

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Stéphane Junca . "Geometric optics with critical vanishing viscosity for one-dimensional semilinear initial value problems." Rev. Mat. Iberoamericana 24 (2) 549 - 566, July, 2008.

Information

Published: July, 2008

First available in Project Euclid: 11 August 2008

zbMATH: 1156.35308

MathSciNet: MR2459203

Subjects:

Primary: 35K45 , 35L60

Secondary: 35B25

Keywords: energy estimates , interpolation , maximum principle , non stationary phase , nonlinear geometric optics , phase , Profile , small viscosity , weakly coupled parabolic systems