scholarly journals Well posedness and asymptotic behavior of a wave equation with distributed time‐delay and Neumann boundary conditions

2019 ◽  
Vol 42 (13) ◽  
pp. 4584-4605
Author(s):  
Boumediène Chentouf ◽  
Aissa Guesmia
Keyword(s):  
Asymptotic Behavior ◽  
Wave Equation ◽  
Time Delay ◽  
Boundary Conditions ◽  
Neumann Boundary ◽  
Neumann Boundary Conditions ◽  
Well Posedness ◽  
Distributed Time Delay

Inverse problems for parabolic equations with interior degeneracy and Neumann boundary conditions

2016 ◽  
Vol 24 (3) ◽  
Author(s):  
Idriss Boutaayamou ◽  
Genni Fragnelli ◽  
Lahcen Maniar
Keyword(s):  
Boundary Conditions ◽  
Parabolic Equations ◽  
Parabolic Problem ◽  
Neumann Boundary ◽  
Spatial Domain ◽  
Neumann Boundary Conditions ◽  
Well Posedness ◽  
Degeneracy Point ◽  
Inverse Source Problems ◽  
Interior Degeneracy

AbstractWe consider a parabolic problem with degeneracy in the interior of the spatial domain and we focus on the well-posedness of the problem and on inverse source problems. The novelties of the present paper are two. First, the degeneracy point is in the interior of the spatial domain. Second, we consider Neumann boundary conditions so that no previous result can be adapted to this situation.

scholarly journals Exact Neumann boundary controllability for problems of transmission of the wave equation

1999 ◽  
Vol 41 (1) ◽  
pp. 125-139 ◽  
Author(s):  
WEIJIU LIU ◽  
GRAHAM H. WILLIAMS
Keyword(s):  
Wave Equation ◽  
Boundary Conditions ◽  
Exact Controllability ◽  
Neumann Boundary ◽  
Neumann Boundary Conditions ◽  
Boundary Controllability ◽  
Hilbert Uniqueness Method ◽  
Uniqueness Method ◽  
Initial States

Using the Hilbert Uniqueness Method, we study the problem of exact controllability in Neumann boundary conditions for problems of transmission of the wave equation. We prove that this system is exactly controllable for all initial states in L2(Ω)×(H1(Ω))′.

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