Multi-Time Systems of Conservation Laws
Aldo Bazan, Paola Loreti, Wladimir Neves
TL;DR
This paper introduces the theory of multi-time systems of conservation laws, establishing existence and uniqueness of solutions for systems with two time variables in one spatial dimension using a generalized Lax-Oleinik formula.
Contribution
It extends conservation law theory to multi-time systems, providing foundational existence and uniqueness results for such systems.
Findings
Proved existence and uniqueness of solutions for multi-time conservation laws.
Generalized the Lax-Oleinik formula to handle multi-time systems.
Focused on systems with two independent time variables in one spatial dimension.
Abstract
Motivated by the work of P.L. Lions and J-C. Rochet [12], concerning multi-time Hamilton-Jacobi equations, we introduce the theory of multi-time systems of conservation laws. We show the existence and uniqueness of solution to the Cauchy problem for a system of multi-time conservation laws with two independent time variables in one space dimension. Our proof relies on a suitable generalization of the Lax-Oleinik formula.
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