Existence and uniqueness of solutions of an asymptotic equation arising from a variational wave equation with general data

Ping Zhang; Yuxi Zheng

doi:10.1007/s205-000-8002-2

Existence and uniqueness of solutions of an asymptotic equation arising from a variational wave equation with general data

Ping Zhang, Yuxi Zheng

Mathematics

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

67 Scopus citations

Abstract

We establish here the global existence and uniqueness of admissible (both dissipative and conservative) weak solutions to a canonical asymptotic equation (∂_t v + u∂_x v + 1/2 v² = 0, v = ∂_xu) for weakly nonlinear solutions of a class of nonlinear variational wave equations with any L²(ℝ) initial datum. We use the method of Young measures and mollification techniques.

Original language	English (US)
Pages (from-to)	49-83
Number of pages	35
Journal	Archive for Rational Mechanics and Analysis
Volume	155
Issue number	1
DOIs	https://doi.org/10.1007/s205-000-8002-2
State	Published - 2000

All Science Journal Classification (ASJC) codes

Analysis
Mathematics (miscellaneous)
Mechanical Engineering

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10.1007/s205-000-8002-2

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title = "Existence and uniqueness of solutions of an asymptotic equation arising from a variational wave equation with general data",

abstract = "We establish here the global existence and uniqueness of admissible (both dissipative and conservative) weak solutions to a canonical asymptotic equation (∂t v + u∂x v + 1/2 v2 = 0, v = ∂xu) for weakly nonlinear solutions of a class of nonlinear variational wave equations with any L2(ℝ) initial datum. We use the method of Young measures and mollification techniques.",

author = "Ping Zhang and Yuxi Zheng",

year = "2000",

doi = "10.1007/s205-000-8002-2",

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T1 - Existence and uniqueness of solutions of an asymptotic equation arising from a variational wave equation with general data

AU - Zhang, Ping

AU - Zheng, Yuxi

PY - 2000

Y1 - 2000

N2 - We establish here the global existence and uniqueness of admissible (both dissipative and conservative) weak solutions to a canonical asymptotic equation (∂t v + u∂x v + 1/2 v2 = 0, v = ∂xu) for weakly nonlinear solutions of a class of nonlinear variational wave equations with any L2(ℝ) initial datum. We use the method of Young measures and mollification techniques.

AB - We establish here the global existence and uniqueness of admissible (both dissipative and conservative) weak solutions to a canonical asymptotic equation (∂t v + u∂x v + 1/2 v2 = 0, v = ∂xu) for weakly nonlinear solutions of a class of nonlinear variational wave equations with any L2(ℝ) initial datum. We use the method of Young measures and mollification techniques.

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U2 - 10.1007/s205-000-8002-2

DO - 10.1007/s205-000-8002-2

M3 - Article

AN - SCOPUS:0034359781

SN - 0003-9527

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SP - 49

EP - 83

JO - Archive for Rational Mechanics and Analysis

JF - Archive for Rational Mechanics and Analysis

IS - 1

ER -

Existence and uniqueness of solutions of an asymptotic equation arising from a variational wave equation with general data

Abstract

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