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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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Contributor : Vincent Perrollaz <>
Submitted on : Thursday, March 14, 2019 - 1:24:21 PM
Last modification on : Saturday, March 16, 2019 - 2:08:09 AM
Long-term archiving on: : Saturday, June 15, 2019 - 7:18:43 PM


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  • HAL Id : hal-02067783, version 1
  • ARXIV : 1903.06448



Rinaldo Colombo, Vincent Perrollaz. Initial Data Identification in Conservation Laws and Hamilton-Jacobi Equations. 2019. ⟨hal-02067783⟩



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