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

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

scholarly journals Energy Pile Field Simulation in Large Buildings: Validation of Surface Boundary Assumptions

2019 ◽  
Author(s):  
Andrea Ferrantelli ◽  
Jevgeni Fadejev ◽  
Jarek Kurnitski
Keyword(s):  
Boundary Conditions ◽  
Single Point ◽  
Ground Surface ◽  
Thermal Mass ◽  
Heat Equations ◽  
Outlet Temperature ◽  
Surface Boundary ◽  
Geothermal Heat ◽  
Soil Medium ◽  
Surface Boundary Conditions

As the energy efficiency demands for future buildings become increasingly stringent, preliminary assessments of energy consumption are mandatory. These are possible only through numerical simulations, whose reliability crucially depends on boundary conditions. We therefore investigate their role in numerical estimates for the usage of geothermal energy, performing annual simulations of transient heat transfer for a building employing a geothermal heat pump plant and energy piles. Starting from actual measurements, we solve the heat equations in 2D and 3D using COMSOL Multiphysics and IDA-ICE, and discover a negligible impact of the multiregional ground surface boundary conditions. Moreover, we verify that the thermal mass of the soil medium induces a small vertical temperature gradient on the piles surface. We also find a roughly constant temperature on each horizontal cross-section, with nearly identical values if the average temperature is integrated over the full plane or evaluated at one single point. Calculating the yearly heating need for an entire building we then show that the chosen upper boundary condition affects the energy balance dramatically. Using directly the pipes’ outlet temperature induces a 54% overestimation of the heat flux, while the exact ground surface temperature above the piles reduces the error to 0.03%.

scholarly journals Energy Pile Field Simulation in Large Buildings: Validation of Surface Boundary Assumptions

Energies ◽  
2019 ◽  
Vol 12 (5) ◽  
pp. 770 ◽  
Author(s):  
Andrea Ferrantelli ◽  
Jevgeni Fadejev ◽  
Jarek Kurnitski
Keyword(s):  
Boundary Conditions ◽  
Single Point ◽  
Ground Surface ◽  
Thermal Mass ◽  
Heat Equations ◽  
Outlet Temperature ◽  
Surface Boundary ◽  
Geothermal Heat ◽  
Soil Medium ◽  
Surface Boundary Conditions

As the energy efficiency demands for future buildings become increasingly stringent, preliminary assessments of energy consumption are mandatory. These are possible only through numerical simulations, whose reliability crucially depends on boundary conditions. We therefore investigate their role in numerical estimates for the usage of geothermal energy, performing annual simulations of transient heat transfer for a building employing a geothermal heat pump plant and energy piles. Starting from actual measurements, we solve the heat equations in 2D and 3D using COMSOL Multiphysics and IDA-ICE, discovering a negligible impact of the multiregional ground surface boundary conditions. Moreover, we verify that the thermal mass of the soil medium induces a small vertical temperature gradient on the piles surface. We also find a roughly constant temperature on each horizontal cross-section, with nearly identical average values when either integrated over the full plane or evaluated at one single point. Calculating the yearly heating need for an entire building, we then show that the chosen upper boundary condition affects the energy balance dramatically. Using directly the pipes’ outlet temperature induces a 54% overestimation of the heat flux, while the exact ground surface temperature above the piles reduces the error to 0.03%.

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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