Semilinear Geometric Optics for Generalized Solutions | Zendy

Yaguang Wang | Zendy; Michael Oberguggenberger | Zendy

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Semilinear Geometric Optics for Generalized Solutions

Author(s) -

Yaguang Wang,

Michael Oberguggenberger

Publication year - 2000

Publication title -

zeitschrift für analysis und ihre anwendungen

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.567

H-Index - 35

eISSN - 1661-4534

pISSN - 0232-2064

DOI - 10.4171/zaa/990

Subject(s) - superposition principle , geometrical optics , nonlinear system , cauchy distribution , mathematics , generalized function , variable (mathematics) , mathematical analysis , space (punctuation) , physics , optics , computer science , quantum mechanics , operating system

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. AMS Subject Classification: 35L45, 35B05, 35D05, 46F30

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