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Zeitschrift für Analysis und ihre Anwendungen

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Volume 19, Issue 4, 2000, pp. 913–926
DOI: 10.4171/ZAA/990

Published online: 2000-12-31

Semilinear Geometric Optics for Generalized Solutions

Ya-Guang Wang[1] and Michael Oberguggenberger[2]

(1) Jiao Tong University, Shanghai, China
(2) Universität Innsbruck, Austria

This paper is devoted to the study of nonlinear geometric optics in Colombeau algebras of generalized functions in the case of Cauchy problems for semilinear hyperbolic systems in one space variable. Extending classical results, we establish a generalized variant of nonlinear geometric optics. As an application, a nonlinear superposition principle is obtained when distributional initial data are perturbed by rapid oscillations.

Keywords: Semilinear hyperbolic systems, Cauchy problems, nonlinear geometric optics, generalized solutions, delta waves

Wang Ya-Guang, Oberguggenberger Michael: Semilinear Geometric Optics for Generalized Solutions. Z. Anal. Anwend. 19 (2000), 913-926. doi: 10.4171/ZAA/990