Electron. J. Differential Equations, Vol. 2022 (2022), No. 78, pp. 1-12.

Extending Lagrangian transformations to nonconvex scalar conservation laws

Prerona Dutta

This article studies a method of finding Lagrangian transformations, in the form of particle paths, for all scalar conservation laws having a smooth flux. These are found using the notion of weak diffeomorphisms. More precisely, from any given scalar conservation law, we derive a Temple system having one linearly degenerate and one genuinely nonlinear family. We modify the system to make it strictly hyperbolic and prove an existence result for it. Finally we establish that entropy admissible weak solutions to this system are equivalent to those of the scalar equation. This method also determines the associated weak diffeomorphism.

Submitted October 24, 2022. Published November 21, 2022.
Math Subject Classifications: 35L65, 35L40, 35L45.
Key Words: Scalar conservation law; Temple system; weak diffeomorphism.

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Prerona Dutta
Department of Mathematics
The Ohio State University
Columbus, OH 43210-1174, USA
email: dutta.105@osu.edu

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