Piecewise smooth solutions to the burgers-hilbert equation

Alberto Bressan; Tianyou Zhang

doi:10.4310/CMS.2017.v15.n1.a7

Piecewise smooth solutions to the burgers-hilbert equation

Alberto Bressan, Tianyou Zhang

Research output: Contribution to journal › Article › peer-review

10 Scopus citations

Abstract

The paper is concerned with the Burgers-Hilbert equation u_t + (u²/2)_x = H[u], where the right-hand side is a Hilbert transform. Unique entropy admissible solutions are constructed locally in time, having a single shock. In a neighborhood of the shock curve, a detailed description of the solution is provided.

Original language	English (US)
Pages (from-to)	165-184
Number of pages	20
Journal	Communications in Mathematical Sciences
Volume	15
Issue number	1
DOIs	https://doi.org/10.4310/CMS.2017.v15.n1.a7
State	Published - 2017

All Science Journal Classification (ASJC) codes

General Mathematics
Applied Mathematics

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10.4310/CMS.2017.v15.n1.a7

Cite this

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abstract = "The paper is concerned with the Burgers-Hilbert equation ut + (u2/2)x = H[u], where the right-hand side is a Hilbert transform. Unique entropy admissible solutions are constructed locally in time, having a single shock. In a neighborhood of the shock curve, a detailed description of the solution is provided.",

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AB - The paper is concerned with the Burgers-Hilbert equation ut + (u2/2)x = H[u], where the right-hand side is a Hilbert transform. Unique entropy admissible solutions are constructed locally in time, having a single shock. In a neighborhood of the shock curve, a detailed description of the solution is provided.

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Piecewise smooth solutions to the burgers-hilbert equation

Abstract

All Science Journal Classification (ASJC) codes

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