The Laplacian with Generalized Wentzell Boundary Conditions

2003 ◽  
pp. 169-180 ◽  
Author(s):  
Angelo Favini ◽  
Gisèle Ruiz Goldstein ◽  
Jerome A. Goldstein ◽  
Enrico Obrecht ◽  
Silvia Romanelli
Keyword(s):  
Boundary Conditions ◽  
Wentzell Boundary Conditions

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 ¯ ) .

scholarly journals Wentzell Boundary Conditions in the Nonsymmetric Case

2008 ◽  
Vol 3 (7) ◽  
pp. 143-147 ◽  
Author(s):  
A. Favini ◽  
G. R. Goldstein ◽  
J. A. Goldstein ◽  
S. Romanelli
Keyword(s):  
Boundary Conditions ◽  
Wentzell Boundary Conditions

Nonautonomous heat equations with generalized Wentzell boundary conditions

2003 ◽  
Vol 3 (2) ◽  
pp. 321-331 ◽  
Author(s):  
Jin Liang ◽  
Rainer Nagel ◽  
Ti-Jun Xiao
Keyword(s):  
Boundary Conditions ◽  
Heat Equations ◽  
Wentzell Boundary Conditions

Cosine families generated by second-order differential operators on W1,1(0, 1) with generalized Wentzell boundary conditions

2005 ◽  
Vol 84 (9) ◽  
pp. 867-876 ◽  
Author(s):  
András Bátkai ◽  
Klaus-Jochen Engel ◽  
Markus Haase
Keyword(s):  
Boundary Conditions ◽  
Differential Operators ◽  
Second Order ◽  
Cosine Families ◽  
Wentzell Boundary Conditions

Analyticity on L 1 of the heat semigroup with Wentzell boundary conditions

2009 ◽  
Vol 94 (1) ◽  
pp. 85-89 ◽  
Author(s):  
Mahamadi Warma
Keyword(s):  
Boundary Conditions ◽  
Heat Semigroup ◽  
Wentzell Boundary Conditions

The non-autonomous wave equation with general Wentzell boundary conditions

2005 ◽  
Vol 135 (2) ◽  
pp. 317-329 ◽  
Author(s):  
Angelo Favini ◽  
Ciprian G. Gal ◽  
Gisèle Ruiz Goldstein ◽  
Jerome A. Goldstein ◽  
Silvia Romanelli
Keyword(s):  
Hilbert Space ◽  
Wave Equation ◽  
Boundary Conditions ◽  
Abstract Cauchy Problem ◽  
Regularity Conditions ◽  
Well Posedness ◽  
One Dimensional ◽  
Wentzell Boundary Conditions ◽  
Image Position ◽  
Dimensional Wave

We study the problem of the well-posedness for the abstract Cauchy problem associated to the non-autonomous one-dimensional wave equation utt = A(t)u with general Wentzell boundary conditions Here A(t)u := (a(x, t)ux)x, a(x, t) ≥ ε > 0 in [0, 1] × [0, + ∞) and βj(t) > 0, γj(t) ≥ 0, (γ0(t), γ1(t)) ≠ (0,0). Under suitable regularity conditions on a, βj, γj we prove the well-posedness in a suitable (energy) Hilbert space

General Wentzell Boundary Conditions and Analytic Semigroups onW1,p(0, 1)

2003 ◽  
Vol 82 (9) ◽  
pp. 927-935 ◽  
Author(s):  
Angelo Favini ◽  
Gisèle Ruiz Goldstein ◽  
Jerome A. Goldstein ◽  
Enrico Obrecht ◽  
Silvia Romanelli
Keyword(s):  
Boundary Conditions ◽  
Analytic Semigroups ◽  
Wentzell Boundary Conditions
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