On the vibrations of rectangular membranes

Vllmos Komornik, H. Brezis

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Abstract

We consider the wave equation in a rectangular domain Cl with homogeneous Dirichlet boundary condition. Let S be an open segment in H, parallel to one of the sides of Ω. We show that if S is shorter than the corresponding side, then for every (arbitrary large) positive number T, there exist smooth initial data such that the corresponding solution of the system is strictly positive in every point of S during the whole time interval (-T, T).

Original languageEnglish (US)
Pages (from-to)319-327
Number of pages9
JournalDifferential and Integral Equations
Volume6
Issue number2
StatePublished - Mar 1993

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All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

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