Asymptotics for wave equations with Wentzell boundary conditions and boundary damping

2016 ◽  
Vol 94 (3) ◽  
pp. 520-531 ◽  
Author(s):  
Chan Li ◽  
Ti-Jun Xiao
Keyword(s):  
Boundary Conditions ◽  
Wave Equations ◽  
Boundary Damping ◽  
Wentzell Boundary Conditions

scholarly journals On a singularly perturbed wave equation with dynamic boundary conditions

2004 ◽  
Vol 134 (2) ◽  
pp. 389-413 ◽  
Author(s):  
Luminiţa Popescu ◽  
Aníbal Rodriguez-Bernal
Keyword(s):  
Boundary Conditions ◽  
Wave Equations ◽  
Limit Problem ◽  
Linear Wave ◽  
Dynamic Boundary Conditions ◽  
Boundary Damping ◽  
Perturbation Problem ◽  
Dynamic Boundary ◽  
Linear Wave Equations ◽  
Parabolic Limit

In this paper we analyse a singular perturbation problem for linear wave equations with interior and boundary damping. We show how the solutions converge to the formal parabolic limit problem with dynamic boundary conditions. Conditions are given for uniform convergence in the energy space.

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 ¯ ) .

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