scholarly journals The large diffusion limit for the heat equation in the exterior of the unit ball with a dynamical boundary condition

2020 ◽  
Vol 40 (11) ◽  
pp. 6529-6546
Author(s):  
Marek Fila ◽  
◽  
Kazuhiro Ishige ◽  
Tatsuki Kawakami ◽  
Johannes Lankeit ◽  
...  
Keyword(s):  
Boundary Condition ◽  
Heat Equation ◽  
Unit Ball ◽  
Diffusion Limit ◽  
Dynamical Boundary Condition ◽  
Large Diffusion

scholarly journals The large diffusion limit for the heat equation with a dynamical boundary condition

2020 ◽  
Vol 23 (01) ◽  
pp. 2050003
Author(s):  
Marek Fila ◽  
Kazuhiro Ishige ◽  
Tatsuki Kawakami
Keyword(s):  
Boundary Condition ◽  
Diffusion Coefficient ◽  
Heat Equation ◽  
Half Space ◽  
Laplace Equation ◽  
Diffusion Limit ◽  
Dynamical Boundary Condition ◽  
Suitable Sense ◽  
Large Diffusion

We study the heat equation on a half-space with a linear dynamical boundary condition. Our main aim is to show that, if the diffusion coefficient tends to infinity, then the solutions converge (in a suitable sense) to solutions of the Laplace equation with the same dynamical boundary condition.

scholarly journals Rate of convergence in the large diffusion limit for the heat equation with a dynamical boundary condition

2019 ◽  
Vol 114 (1-2) ◽  
pp. 37-57 ◽  
Author(s):  
Marek Fila ◽  
Kazuhiro Ishige ◽  
Tatsuki Kawakami ◽  
Johannes Lankeit
Keyword(s):  
Boundary Condition ◽  
Heat Equation ◽  
Rate Of Convergence ◽  
Diffusion Limit ◽  
Dynamical Boundary Condition ◽  
Large Diffusion

scholarly journals PARABOLIC PROBLEMS WITH DYNAMICAL BOUNDARY CONDITIONS IN PERFORATED MEDIA

2003 ◽  
Vol 8 (4) ◽  
pp. 337-350 ◽  
Author(s):  
C. Timofte
Keyword(s):  
Boundary Condition ◽  
Asymptotic Behavior ◽  
Boundary Value Problem ◽  
Heat Equation ◽  
Dirichlet Condition ◽  
Parabolic Problems ◽  
Perforated Domain ◽  
Limit Equation ◽  
Dynamical Boundary Condition ◽  
Dynamical Boundary Conditions

The asymptotic behavior of the solution of a parabolic dynamical boundary‐value problem in a periodically perforated domain is analyzed. The perforations, which are identical and periodically distributed, are of size ϵ. In the perforated domain we consider a heat equation, with a Dirichlet condition on the exterior boundary and a dynamical boundary condition on the surface of the holes. The limit equation, as ϵ ? 0, is a heat equation with extra-terms coming from the influence of the non-homogeneous dynamical boundary condition.

On the Dispersive Estimate for the Dirichlet Schrödinger Propagator and Applications to Energy Critical NLS

2014 ◽  
Vol 66 (5) ◽  
pp. 1110-1142
Author(s):  
Dong Li ◽  
Guixiang Xu ◽  
Xiaoyi Zhang
Keyword(s):  
Boundary Condition ◽  
Fundamental Solution ◽  
Unit Ball ◽  
Dirichlet Boundary Condition ◽  
Obstacle Problem ◽  
Dirichlet Boundary ◽  
Radial Symmetry ◽  
Well Posedness ◽  
Robust Algorithm ◽  
Dispersive Estimate

AbstractWe consider the obstacle problem for the Schrödinger evolution in the exterior of the unit ball with Dirichlet boundary condition. Under radial symmetry we compute explicitly the fundamental solution for the linear Dirichlet Schrödinger propagator and give a robust algorithm to prove sharp L1 → L∞ dispersive estimates. We showcase the analysis in dimensions n = 5, 7. As an application, we obtain global well–posedness and scattering for defocusing energy-critical NLS on with Dirichlet boundary condition and radial data in these dimensions.

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