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

Ping Zhang, Yuxi Zheng

Research output: Contribution to journalArticle

52 Citations (Scopus)

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 languageEnglish (US)
Pages (from-to)49-83
Number of pages35
JournalArchive for Rational Mechanics and Analysis
Volume155
Issue number1
DOIs
StatePublished - Jan 1 2000

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Variational Equation
Wave equations
Existence and Uniqueness of Solutions
Wave equation
Young Measures
Global Existence
Weak Solution
Existence and Uniqueness
Class

All Science Journal Classification (ASJC) codes

  • Analysis
  • Mathematics (miscellaneous)
  • Mechanical Engineering

Cite this

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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.",
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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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