Nonlinear geometric optics for hyperbolic systems of conservation laws. (English) Zbl 0622.65117

Oscillation theory, computation, and methods of compensated compactness, Proc. Workshop, Minneapolis/Minn. 1984/85, IMA Vol. Math. Appl. 2, 115-165 (1986).
[For the entire collection see Zbl 0594.00008.]
In this research report the author gives a thorough discussion of recent works in the theory of weakly nonlinear geometric optics for constructing asymptotic solutions of quasilinear hyperbolic systems in one and several space variables. Mainly the report is devoted to a detailed discussion and description of formal perturbation methods (i.e., the methods developed through systematic self-consistent perturbation schemes for resonant and nonresonant wave problems) applied to problems in one and several space dimensions. Towards the end the report includes a small but adequate discussion and description of rigorous analysis on the use of weakly nonlinear geometric optics for systems in one space dimension.
Reviewer: V.P.Tyagi


65Z05 Applications to the sciences
35L65 Hyperbolic conservation laws
78A05 Geometric optics


Zbl 0594.00008