Global existence of weak solutions for the burgers-hilbert equation

Alberto Bressan; Khai T. Nguyen

doi:10.1137/140957536

Global existence of weak solutions for the burgers-hilbert equation

Alberto Bressan, Khai T. Nguyen

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

18 Scopus citations

Abstract

This paper establishes the global existence of weak solutions to the Burgers-Hilbert equation, for general initial data in L² (ℝ). For positive times, the solution lies in L² ∩ L∞ . A partial uniqueness result is proved for spatially periodic solutions, as long as the total variation remains locally bounded.

Original language	English (US)
Pages (from-to)	2884-2904
Number of pages	21
Journal	SIAM Journal on Mathematical Analysis
Volume	46
Issue number	4
DOIs	https://doi.org/10.1137/140957536
State	Published - 2014

All Science Journal Classification (ASJC) codes

Analysis
Computational Mathematics
Applied Mathematics

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10.1137/140957536

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title = "Global existence of weak solutions for the burgers-hilbert equation",

abstract = "This paper establishes the global existence of weak solutions to the Burgers-Hilbert equation, for general initial data in L2 (ℝ). For positive times, the solution lies in L2 ∩ L∞ . A partial uniqueness result is proved for spatially periodic solutions, as long as the total variation remains locally bounded.",

author = "Alberto Bressan and Nguyen, {Khai T.}",

note = "Funding Information: This research was partially supported by NSF, with grant DMS-1411786 {"}Hyperbolic Conservation Laws and Applications.{"} Publisher Copyright: {\textcopyright} 2014 Society for Industrial and Applied Mathematics.",

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AU - Bressan, Alberto

AU - Nguyen, Khai T.

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PY - 2014

Y1 - 2014

N2 - This paper establishes the global existence of weak solutions to the Burgers-Hilbert equation, for general initial data in L2 (ℝ). For positive times, the solution lies in L2 ∩ L∞ . A partial uniqueness result is proved for spatially periodic solutions, as long as the total variation remains locally bounded.

AB - This paper establishes the global existence of weak solutions to the Burgers-Hilbert equation, for general initial data in L2 (ℝ). For positive times, the solution lies in L2 ∩ L∞ . A partial uniqueness result is proved for spatially periodic solutions, as long as the total variation remains locally bounded.

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Global existence of weak solutions for the burgers-hilbert equation

Abstract

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