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arXiv · 2305.08427

Peculiarities of Space Dependent Conservation Laws: Inverse Design and Asymptotics

Rinaldo M. Colombo·Vincent Perrollaz·Abraham Sylla
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Abstract

Recently, results regarding the Inverse Design problem for Conservation Laws and Hamilton-Jacobi equations with space-dependent convex fluxes were obtaine. More precisely, characterizations of attainable sets and the set of initialdata evolving at a prescribed time into a prescribed profile were obtained. Here, wepresent an explicit example that underlines deep diff erences between the space-dependentand space-independent cases. Moreover, we add a detailed analysis of the time asymptoticsolution of this example, again underlining diff erences with the space-independent case.

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Rinaldo M. Colombo, Vincent Perrollaz, Abraham Sylla. 2023-05-15. Peculiarities of Space Dependent Conservation Laws: Inverse Design and Asymptotics. https://arxiv.org/abs/2305.08427

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