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

scholarly journals On a Generalization of One-Dimensional Kinetics

Mathematics ◽  
2021 ◽  
Vol 9 (11) ◽  
pp. 1264
Author(s):  
Vladimir V. Uchaikin ◽  
Renat T. Sibatov ◽  
Dmitry N. Bezbatko
Keyword(s):  
Exact Solution ◽  
Asymptotic Behavior ◽  
Constant Velocity ◽  
Telegraph Equation ◽  
Material Derivative ◽  
Symmetric Random Walk ◽  
One Dimensional ◽  
Special Cases ◽  
Fractional Telegraph Equation ◽  
Asymmetric Case

One-dimensional random walks with a constant velocity between scattering are considered. The exact solution is expressed in terms of multiple convolutions of path-distributions assumed to be different for positive and negative directions of the walk axis. Several special cases are considered when the convolutions are expressed in explicit form. As a particular case, the solution of A. S. Monin for a symmetric random walk with exponential path distribution and its generalization to the asymmetric case are obtained. Solution of fractional telegraph equation with the fractional material derivative is presented. Asymptotic behavior of its solution for an asymmetric case is provided.

scholarly journals Limit of 𝑝-Laplacian obstacle problems

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Raffaela Capitanelli ◽  
Maria Agostina Vivaldi
Keyword(s):  
Asymptotic Behavior ◽  
Uniform Convergence ◽  
Explicit Expression ◽  
Positive Measure ◽  
Sufficient Conditions ◽  
Obstacle Problems ◽  
Dimensional Case ◽  
Asymptotic Behavior Of Solutions ◽  
One Dimensional ◽  
The One

AbstractIn this paper, we study asymptotic behavior of solutions to obstacle problems for p-Laplacians as {p\to\infty}. For the one-dimensional case and for the radial case, we give an explicit expression of the limit. In the n-dimensional case, we provide sufficient conditions to assure the uniform convergence of the whole family of the solutions of obstacle problems either for data f that change sign in Ω or for data f (that do not change sign in Ω) possibly vanishing in a set of positive measure.

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