Applied Mathematics and Optimization

, Volume 7, Issue 1, pp 35–93 | Cite as

A cosine operator approach to modelingL2(0,T; L2 (Γ))—Boundary input hyperbolic equations

  • I. Lasiecka
  • R. Triggiani
Article
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Abstract

This paper investigates the regularity properties of the solution of a second-order hyperbolic equation defined over a bounded domain Ω with boundary Γ, under the action of a boundary forcing term inL2(0,T; L2(Γ)). Both Dirichlet and Neumann nonhomogeneous cases are considered. A functional analytic model based on cosine operator functions is presented, which provides an input-solution formula to be interpreted in appropriate topologies. With the help of this model, it is shown, for example, that the solution of the nonhomogeneous Dirichlet problem is inL2(0,T; L2(Ω)), when Ω is either a parallelepiped or a sphere, while the solution of the nonhomogeneous Neumann problem is inL2(0,T; H3/4-e(Ω)) when Ω is a parallelepiped and inL2(0,T; H2/3(Ω) when Ω is a sphere. The Dirichlet case for general domains is studied by means of pseudodifferential operator techniques.

Keywords

Bounded Domain Operator Technique Dirichlet Problem Operator Function Operator Approach 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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Copyright information

© Springer-Verlag New York Inc. 1981

Authors and Affiliations

  • I. Lasiecka
    • 1
  • R. Triggiani
    • 2
  1. 1.Department of System ScienceUniversity of CaliforniaLos AngelesUSA
  2. 2.Department of MathematicsIowa State UniversityAmesUSA

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