Revista Matemática Iberoamericana


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Volume 24, Issue 2, 2008, pp. 549–566
DOI: 10.4171/RMI/546

Published online: 2008-08-31

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

Stéphane Junca[1]

(1) Université de Nice Sophia Antipolis, France

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.

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

Junca Stéphane: Geometric optics with critical vanishing viscosity for one-dimensional semilinear initial value problems. Rev. Mat. Iberoamericana 24 (2008), 549-566. doi: 10.4171/RMI/546