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

Stéphane Junca

Source: Rev. Mat. Iberoamericana Volume 24, Number 2 (2008), 549-566.

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.

Primary Subjects: 35K45, 35L60

Secondary Subjects: 35B25

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

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