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Mathematics > Differential Geometry

arXiv:1512.04990 (math)
[Submitted on 15 Dec 2015]

Title:Shape maps for second order partial differential equations

Authors: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.
Subjects: Differential Geometry (math.DG); Analysis of PDEs (math.AP)
MSC classes: 58J47, 58J60, 58A20, 35G50, 35N99
Cite as: arXiv:1512.04990 [math.DG]
  (or arXiv:1512.04990v1 [math.DG] for this version)
  https://doi.org/10.48550/arXiv.1512.04990
Related DOI: https://doi.org/10.1016/j.matpur.2016.07.010

Submission history

From: Geoffrey Prince [view email]
[v1] Tue, 15 Dec 2015 22:26:41 UTC (533 KB)
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