scholarly journals The regularity of pullback attractor for a non-autonomous p-Laplacian equation with dynamical boundary condition

2019 ◽  
Vol 24 (2) ◽  
pp. 529-546
Author(s):  
Wen Tan ◽  
◽  
Keyword(s):  
Boundary Condition ◽  
Pullback Attractor ◽  
Dynamical Boundary Condition ◽  
Laplacian Equation

BLOW-UP ANALYSIS FOR SOLUTIONS OF THE LAPLACIAN EQUATION WITH EXPONENTIAL NEUMANN BOUNDARY CONDITION IN DIMENSION TWO

2006 ◽  
Vol 08 (06) ◽  
pp. 737-761 ◽  
Author(s):  
YU-XIA GUO ◽  
JIA-QUAN LIU
Keyword(s):  
Boundary Condition ◽  
Asymptotic Behavior ◽  
Existence Theorem ◽  
Neumann Boundary Condition ◽  
Blow Up ◽  
Neumann Boundary ◽  
Asymptotic Behavior Of Solutions ◽  
Laplacian Equation ◽  
Blow Up Analysis

We consider the asymptotic behavior of solutions of the Laplacian equation with exponential Neumann boundary condition in dimension two. As an application, we prove an existence theorem of nonminimum solutions.

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.

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