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arXiv · 1903.06448

Initial Data Identification in Conservation Laws and Hamilton-Jacobi Equations

Rinaldo Colombo·Vincent Perrollaz
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Abstract

In the scalar 1D case, conservation laws and Hamilton-Jacobi equations are deeply related. For both, we characterize those profiles that can be attained as solutions at a given positive time corresponding to at least one initial datum. Then, for each of the two equations, we precisely identify all those initial data yielding a solution that coincide with a given profile at that positive time. Various topological and geometrical properties of the set of these initial data are then proved. 2000 Mathematics Subject Classification: 35L65, 35F21, 93B30, 35R30.

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Rinaldo Colombo, Vincent Perrollaz. 2019-03-15. Initial Data Identification in Conservation Laws and Hamilton-Jacobi Equations. https://arxiv.org/abs/1903.06448

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