Recovering a potential in damped wave equation from Dirichlet-to-Neumann operator

2021 ◽  
Author(s):  
Alemdar Hasanov ◽  
Vladimir G Romanov
Keyword(s):  
Wave Equation ◽  
Damped Wave Equation ◽  
Neumann Operator ◽  
Dirichlet To Neumann Operator

scholarly journals Global existence and dynamic structure of solutions for damped wave equation involving the fractional Laplacian

2021 ◽  
Vol 54 (1) ◽  
pp. 245-258
Author(s):  
Younes Bidi ◽  
Abderrahmane Beniani ◽  
Khaled Zennir ◽  
Ahmed Himadan
Keyword(s):  
Wave Equation ◽  
Global Solution ◽  
Fractional Laplacian ◽  
Necessary Conditions ◽  
Dynamic Structure ◽  
Decay Estimates ◽  
Damped Wave Equation ◽  
Structure Of Solutions ◽  
Nonlinear Source ◽  
Galerkin Approximations

Abstract We consider strong damped wave equation involving the fractional Laplacian with nonlinear source. The results of global solution under necessary conditions on the critical exponent are established. The existence is proved by using the Galerkin approximations combined with the potential well theory. Moreover, we showed new decay estimates of global solution.

scholarly journals Analytic semigroups generated by Dirichlet-to-Neumann operators on manifolds

2021 ◽  
Author(s):  
Tim Binz
Keyword(s):  
Boundary Conditions ◽  
Elliptic Operator ◽  
Compact Manifold ◽  
Analytic Semigroup ◽  
Continuous Functions ◽  
Analytic Semigroups ◽  
Abstract Theory ◽  
Neumann Operator ◽  
Wentzell Boundary Conditions ◽  
Dirichlet To Neumann Operator

AbstractWe consider the Dirichlet-to-Neumann operator associated to a strictly elliptic operator on the space $$\mathrm {C}(\partial M)$$ C ( ∂ M ) of continuous functions on the boundary $$\partial M$$ ∂ M of a compact manifold $$\overline{M}$$ M ¯ with boundary. We prove that it generates an analytic semigroup of angle $$\frac{\pi }{2}$$ π 2 , generalizing and improving a result of Escher with a new proof. Combined with the abstract theory of operators with Wentzell boundary conditions developed by Engel and the author, this yields that the corresponding strictly elliptic operator with Wentzell boundary conditions generates a compact and analytic semigroups of angle $$\frac{\pi }{2}$$ π 2 on the space $$\mathrm {C}(\overline{M})$$ C ( M ¯ ) .

Golbal nonexistence in a nonlinearly damped wave equation

2001 ◽  
Vol 80 (3-4) ◽  
pp. 269-277 ◽  
Author(s):  
Salim A. Messaoudi
Keyword(s):  
Wave Equation ◽  
Damped Wave Equation
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