scholarly journals On a mixed problem for d'Alembertian with a mixed boundary condition. An example of moving boundary

1975 ◽  
Vol 11 (2) ◽  
pp. 339-401 ◽  
Author(s):  
Atsushi Inoue
Keyword(s):  
Boundary Condition ◽  
Mixed Problem ◽  
Moving Boundary ◽  
Mixed Boundary Condition ◽  
Mixed Boundary

scholarly journals Boundary value controllability and observability problems for the wave and heat equation

1988 ◽  
Vol 29 (4) ◽  
pp. 461-479
Author(s):  
K.-D. Werner
Keyword(s):  
Boundary Condition ◽  
Heat Equation ◽  
Mixed Boundary Condition ◽  
Mixed Boundary ◽  
Finite Energy ◽  
Duality Principle ◽  
Spherical Region ◽  
Initial States ◽  
The Fourier Transform ◽  
Controllability And Observability

AbstractIn this paper, we study controllability and observability problems for the wave and heat equation in a spherical region in Rn, where the control enters in the mixed boundary condition. In the main result, we show that all “finite energy” initial states (i.e. (ω0, ν0) ∈ H1(Ω) × L2 (Ω)) can be steered to zero at time T, using a control f ∈ L2 (∂Ω × [0, T]), provided T > 2. On this basis, we use the duality principle to investigate initial observability for the wave equation. Applying the Fourier transform technique, we obtain controllability and observability results for the heat equation.

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