Journal Articles Journal de Mathématiques Pures et Appliquées Year : 2020

Initial Data Identification in Conservation Laws and Hamilton-Jacobi Equations

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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Dates and versions

hal-02067783 , version 1 (14-03-2019)

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Rinaldo M. Colombo, Vincent Perrollaz. Initial Data Identification in Conservation Laws and Hamilton-Jacobi Equations. Journal de Mathématiques Pures et Appliquées, 2020, 138, pp.1-27. ⟨10.1016/j.matpur.2020.03.005⟩. ⟨hal-02067783⟩
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