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Abstract We prove a unique continuation property for the wave eqiuation in a time-dependent domain Ω ( t ) , 0 ≤ t ≤ T . That is, if u… Click to show full abstract
Abstract We prove a unique continuation property for the wave eqiuation in a time-dependent domain Ω ( t ) , 0 ≤ t ≤ T . That is, if u ( t ) is a finite energy solution of the equation u t t − Δ u = 0 , x ∈ Ω ( t ) , with u ( x , t ) | ∂ Ω ( t ) = 0 , 0 ≤ t ≤ T , satisfying u ( t ) = 0 on some neighbourhood ω ( t ) of a portion of the boundary ∂ Ω ( t ) , 0 ≤ t ≤ T , then we have u ( t ) = 0 on Ω ( t ) , 0 ≤ t ≤ T , under the assumptions that T is sufficiently large and Ω ( t ) does not move so rapidly.
Keywords:
unique continuation;
continuation property;
property wave;
time dependent;
dependent domain
Journal Title: Journal of Mathematical Analysis and Applications
Year Published: 2022
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Journal Title: Journal of Mathematical Analysis and Applications
Year Published: 2022
Link to full text (if available)
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recommendations!