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2004 Focusing of spherical nonlinear pulses in {$R\sp {1+3}$}, III. Sub and supercritical cases
Rémi Carles, Jeffrey Rauch
Tohoku Math. J. (2) 56(3): 393-410 (2004). DOI: 10.2748/tmj/1113246675

Abstract

We study the validity of geometric optics in $L^\infty$ for nonlinear wave equations in three space dimensions whose solutions, pulse like, focus at a point. If the amplitude of the initial data is subcritical, then no nonlinear effect occurs at leading order. If the amplitude of the initial data is sufficiently big, then strong nonlinear effects occur; we study the cases where the equation is either dissipative or accretive. When the equation is dissipative, pulses are absorbed before reaching the focal point. When the equation is accretive, the family of pulses becomes unbounded.

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Rémi Carles. Jeffrey Rauch. "Focusing of spherical nonlinear pulses in {$R\sp {1+3}$}, III. Sub and supercritical cases." Tohoku Math. J. (2) 56 (3) 393 - 410, 2004. https://doi.org/10.2748/tmj/1113246675

Information

Published: 2004
First available in Project Euclid: 11 April 2005

zbMATH: 1095.35010
MathSciNet: MR2075774
Digital Object Identifier: 10.2748/tmj/1113246675

Subjects:
Primary: 35L70
Secondary: 35B25, 35B33, 35B40, 35L20, 35Q60

Rights: Copyright © 2004 Tohoku University

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