scholarly journals Asymptotic behavior for a nonlocal diffusion equation in exterior domains: The critical two-dimensional case

2016 ◽  
Vol 436 (1) ◽  
pp. 586-610 ◽  
Author(s):  
C. Cortázar ◽  
M. Elgueta ◽  
F. Quirós ◽  
N. Wolanski
Keyword(s):  
Asymptotic Behavior ◽  
Diffusion Equation ◽  
Nonlocal Diffusion ◽  
Dimensional Case ◽  
Two Dimensional ◽  
Exterior Domains

scholarly journals Asymptotic Behavior for a One-Dimensional Nonlocal Diffusion Equation in Exterior Domains

2016 ◽  
Vol 48 (3) ◽  
pp. 1549-1574 ◽  
Author(s):  
Carmen Cortázar ◽  
Manuel Elgueta ◽  
Fernando Quirós ◽  
Noemí Wolanski
Keyword(s):  
Asymptotic Behavior ◽  
Diffusion Equation ◽  
Nonlocal Diffusion ◽  
Exterior Domains ◽  
One Dimensional

scholarly journals Asymptotic Behavior for a Nonlocal Diffusion Equation in Domains with Holes

2012 ◽  
Vol 205 (2) ◽  
pp. 673-697 ◽  
Author(s):  
Carmen Cortázar ◽  
Manuel Elgueta ◽  
Fernando Quirós ◽  
Noemí Wolanski
Keyword(s):  
Asymptotic Behavior ◽  
Diffusion Equation ◽  
Nonlocal Diffusion

scholarly journals Asymptotic behavior for a nonlocal diffusion equation on the half line

2015 ◽  
Vol 35 (4) ◽  
pp. 1391-1407 ◽  
Author(s):  
Carmen Cortázar ◽  
◽  
Manuel Elgueta ◽  
Fernando Quirós ◽  
Noemí Wolanski ◽  
...  
Keyword(s):  
Asymptotic Behavior ◽  
Diffusion Equation ◽  
Nonlocal Diffusion ◽  
Half Line

ON THE ASYMPTOTIC BEHAVIOR OF HEATING TIMES

2003 ◽  
Vol 01 (04) ◽  
pp. 429-432 ◽  
Author(s):  
CHIN-HUEI CHANG ◽  
YUN SHYONG CHOW ◽  
ZHEN WANG
Keyword(s):  
Asymptotic Behavior ◽  
Heat Conduction ◽  
Differential Equations ◽  
Heat Conduction Problem ◽  
Asymptotic Expression ◽  
Waiting Times ◽  
Dimensional Case ◽  
Two Dimensional ◽  
Zero Temperature ◽  
A Value

An infinite homogeneous d-dimensional medium initially is at zero temperature, u=0. A heat impulse is applied at the origin, raising the temperature there to a value greater than a constant value u0>0. The temperature at the origin then decays, and when it reaches u0, another equal-sized heat impulse is applied at a normalized time τ1=1. Subsequent equal-sized heat impulses are applied at the origin at the normalized times τn, n=2,3,…, when the temperature there has decayed to u0. This sequence of normalized waiting times τn can be defined recursively by [Formula: see text] where d>0. This heat conduction problem was studied by Myshkis (J. Differential Equations Appl.3 (1997), 89–91), and he posed the problem to find an asymptotic expression for the τn as n→∞. The cases for dimensions d=1 and d≥3 have been treated by Chen, Chow, and Hsieh (J. Differential Equations Appl.6 (2000), 309–318). Here, we deal with the two-dimensional case, d=2.

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