The lifespan of solutions to nonlinear systems of a high-dimensional wave equation

Vladimir Simeonov Gueorguiev, Hiroyuki Takamura, Zhou Yi

Research output: Contribution to journalArticle

13 Citations (Scopus)

Abstract

In this work we study the lifespan of solutions to a p-q system in the higher-dimensional case n≥4. A suitable local existence curve in the p-q plane is found. The curve characterizes the local solutions in Sobolev space Hs with s≥0. Further, some lower and upper bounds of the lifespan of classical solutions are found too. This work is an extension of work [Geometric Optics and Related Topics, Progress in Nonlinear Differential Equations and their Applications, vol. 32, Birkhäuser, Basel, 1997, pp. 117-140], where a suitable global existence small data curve is studied. In the subcritical case, we give almost precise results for the lower bounds of the lifespan by using a suitable weighted Strichartz estimate for the higher-dimensional wave equation.

Original languageEnglish
Pages (from-to)2215-2250
Number of pages36
JournalNonlinear Analysis, Theory, Methods and Applications
Volume64
Issue number10
DOIs
Publication statusPublished - 2006 May 15
Externally publishedYes

Fingerprint

Sobolev spaces
Life Span
Wave equations
Nonlinear systems
Wave equation
Optics
Differential equations
High-dimensional
Nonlinear Systems
Curve
Geometric Optics
Strichartz Estimates
Weighted Estimates
Local Existence
Local Solution
Classical Solution
Global Existence
Sobolev Spaces
Nonlinear Differential Equations
Upper and Lower Bounds

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics
  • Mathematics(all)

Cite this

The lifespan of solutions to nonlinear systems of a high-dimensional wave equation. / Gueorguiev, Vladimir Simeonov; Takamura, Hiroyuki; Yi, Zhou.

In: Nonlinear Analysis, Theory, Methods and Applications, Vol. 64, No. 10, 15.05.2006, p. 2215-2250.

Research output: Contribution to journalArticle

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