Geodesic
On the set of limit values of local diffeomorphisms in wavefront evolution
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 16 (2010) no. 1, pp. 171-185

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We study the problem of the appearance of nonsmooth singularities in the evolution of plane wavefronts in the Dirichlet problem for a first-order partial differential equation. The approach to investigating the singularities is based on the properties of local diffeomorphisms. A generalization of the classical notion of a derivative is introduced, which coincides in particular cases with the Schwarz derivative. The results of modeling solutions of nonsmooth dynamic problems are presented.
Keywords: first-order partial differential equation, minimax solution, diffeomorphism, optimal result function, symmetry set.
Mots-clés : eikonal 
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A. A. Uspenskii; P. D. Lebedev. On the set of limit values of local diffeomorphisms in wavefront evolution. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 16 (2010) no. 1, pp. 171-185. http://geodesic.mathdoc.fr/item/TIMM_2010_16_1_a13/