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arXiv · 1512.04990

Shape maps for second order partial differential equations

O. Rossi·D. J. Saunders·G. E. Prince
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Abstract

We analyse the singularity formation of congruences of solutions of systems of second order PDEs via the construction of \emph{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. We develop the necessary geometric framework on a suitable jet space in which the shape maps appear naturally associated with certain linear connections. Explicit computations are given, along with a nontrivial example.

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O. Rossi, D. J. Saunders, G. E. Prince. 2015-12-15. Shape maps for second order partial differential equations. https://doi.org/10.1016/j.matpur.2016.07.010

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