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Using \(K\)-branch entropy solutions for multivalued geometric optics computations. (English) Zbl 0999.78003
Summary: This paper is devoted to a numerical simulation of the classical WKB system arising in geometric optics expansions. It contains the nonlinear eikonal equation and a linear conservation law whose coefficient can be discontinuous. We address the problem of treating it in such a way that superimposed signals can be reproduced by means of the kinetic formulation of “multibranch solutions”, originally due to Y. Brenier and L. Corrias [Ann. Inst. Henri Poincaré, Anal. Non Linéaire 15, No. 2, 169–190 (1998; Zbl 0893.35068)]. Some existence and uniqueness results are given, together with computational test cases of increasing difficulty displaying up to five multivaluations.

MSC:
78A05 Geometric optics
35Q60 PDEs in connection with optics and electromagnetic theory
35C05 Solutions to PDEs in closed form
35Q40 PDEs in connection with quantum mechanics
35Q53 KdV equations (Korteweg-de Vries equations)
65M99 Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems
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