scholarly journals Heat Content Asymptotics for Riemannian Manifolds with Zaremba Boundary Conditions

2007 ◽  
Vol 26 (3) ◽  
pp. 225-254 ◽  
Author(s):  
M. van den Berg ◽  
P. Gilkey ◽  
K. Kirsten ◽  
V. A. Kozlov
Keyword(s):  
Boundary Conditions ◽  
Riemannian Manifolds ◽  
Heat Content ◽  
Heat Content Asymptotics

The heat content asymptotics of a time-dependent process

2000 ◽  
Vol 130 (2) ◽  
pp. 307-312 ◽  
Author(s):  
M. van den Berg ◽  
P. Gilkey
Keyword(s):  
Heat Source ◽  
Boundary Conditions ◽  
Compact Manifold ◽  
Smooth Boundary ◽  
Heat Content ◽  
Time Dependent ◽  
Time Dependent Process ◽  
Dependent Process ◽  
Heat Content Asymptotics

Let M be a compact manifold with smooth boundary. We study the heat content asymptotics on M defined by a time-dependent heat source and time-dependent boundary conditions.

HEAT CONTENT ASYMPTOTICS OF AN INHOMOGENEOUS TIME-DEPENDENT PROCESSES

2000 ◽  
Vol 15 (18) ◽  
pp. 1165-1179 ◽  
Author(s):  
PETER GILKEY ◽  
JEONG HYEONG PARK
Keyword(s):  
Heat Source ◽  
Boundary Conditions ◽  
Specific Heat ◽  
Compact Manifold ◽  
Smooth Boundary ◽  
Heat Content ◽  
Time Dependent ◽  
Heat Content Asymptotics ◽  
Dependent Processes

Let M be a compact manifold with smooth boundary. We study the heat content asymptotics on M which are defined by a time-dependent metric gt, by a time-dependent heat source, by time-dependent boundary conditions, and by a time-dependent specific heat.

scholarly journals Short-time heat diffusion in compact domains with discontinuous transmission boundary conditions

2015 ◽  
Vol 26 (01) ◽  
pp. 59-110 ◽  
Author(s):  
Claude Bardos ◽  
Denis Grebenkov ◽  
Anna Rozanova-Pierrat
Keyword(s):  
Asymptotic Expansion ◽  
Boundary Conditions ◽  
Order Term ◽  
Heat Content ◽  
Resistance Coefficient ◽  
Small Time ◽  
Heat Diffusion ◽  
Heat Problem ◽  
Short Time ◽  
Mathematical Justification

We consider a heat problem with discontinuous diffusion coefficients and discontinuous transmission boundary conditions with a resistance coefficient. For all bounded (ϵ, δ)-domains Ω ⊂ ℝn with a d-set boundary (for instance, a self-similar fractal), we find the first term of the small-time asymptotic expansion of the heat content in the complement of Ω, and also the second-order term in the case of a regular boundary. The asymptotic expansion is different for the cases of finite and infinite resistance of the boundary. The derived formulas relate the heat content to the volume of the interior Minkowski sausage and present a mathematical justification to the de Gennes' approach. The accuracy of the analytical results is illustrated by solving the heat problem on prefractal domains by a finite elements method.

Heat content asymptotics

2002 ◽  
Vol 104 (1-3) ◽  
pp. 185-188 ◽  
Author(s):  
JeongHyeong Park ◽  
Peter B. Gilkey
Keyword(s):  
Heat Content ◽  
Heat Content Asymptotics
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