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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.

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
Full Text: DOI
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