Shape maps for second order partial differential equations. (English. French summary) Zbl 1375.58025
The paper deals with the singularity formation of congruences of solutions of systems of second order PDEs via the construction of shape maps. The trace of such maps represents a congruence volume whose collapse we study through an appropriate evolution equation, akin to Raychaudhuri’s equation. The authors develop the necessary geometric framework on a suitable jet space in which the shape maps appear naturally associated with certain linear connections. The paper contains explicit computations, a nontrivial example is given.
Reviewer: Yuri E. Gliklikh (Voronezh)
MSC:
| 58J60 | Relations of PDEs with special manifold structures (Riemannian, Finsler, etc.) |
| 58A20 | Jets in global analysis |
| 35G50 | Systems of nonlinear higher-order PDEs |
| 35N99 | Overdetermined problems for partial differential equations and systems of partial differential equations |
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