JournalszaaVol. 19, No. 4pp. 913–926

Semilinear Geometric Optics for Generalized Solutions

  • Ya-Guang Wang

    Jiao Tong University, Shanghai, China
  • Michael Oberguggenberger

    Universität Innsbruck, Austria
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Abstract

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.

Cite this article

Ya-Guang Wang, Michael Oberguggenberger, Semilinear Geometric Optics for Generalized Solutions. Z. Anal. Anwend. 19 (2000), no. 4, pp. 913–926

DOI 10.4171/ZAA/990