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Information Center for Mathematical Science

논문검색

Information Center for Mathematical Science

논문검색

Tohoku Mathematical Journal. Second Series
( Vol. 56 NO.3 / (2004))
Focusing of spherical Nonlinear Pulses in $R^1+3$, III. Sub and Supercritical Cases
Remi Carles, Jeffrey Rauch,
Pages. 393-410
Abstract
Contents 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 ono 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.
Key words Geometric optics, short pulses, focusing, caustic, high frequency asymptotics
Mathmatical Subject Classification 35B40, 35B25, 35B33, 35L05, 35