Singularities in Boundary Value Problems and Exact Controllability of Hyperbolic Systems

doi:https://doi.org/10.1007/978-3-0348-8625-3_8

Singularities in Boundary Value Problems and Exact Controllability of Hyperbolic Systems

Pierre Grisvard-1992-01-01-Birkhäuser Basel eBooks

8

TL;DRAbstract

For simplicity we consider control by the Dirichlet data of the solutions of the wave equation. One considers a bounded open subset Ω of ℝn with boundary Γ = ∂Ω (assumed to be at least Lipschitz). We denote by Q the cylinder Ω×]O, T[ and by ∑=Γ×]O,T[ its lateral boundary. We denote by a mere differentiation in t∈]O,T[ and u(O) denotes the function u at time t=O.

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For simplicity we consider control by the Dirichlet data of the solutions of the wave equation. One considers a bounded open subset Ω of ℝn with boundary Γ = ∂Ω (assumed to be at least Lipschitz). We denote by Q the cylinder Ω×]O, T[ and by ∑=Γ×]O,T[ its lateral boundary. We denote by a mere differentiation in t∈]O,T[ and u(O) denotes the function u at time t=O.

Keywords

MathematicsBounded functionLipschitz continuityGravitational singularityMathematical analysisControllabilityBoundary (topology)Simplicity

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