The asymptotic behavior of solution for the singularly perturbed initial boundary value problems of the reaction diffusion equations in a part of domain

2001 ◽  
Vol 22 (10) ◽  
pp. 1192-1197
Author(s):  
Liu Qi-lin ◽  
Mo Jia-qi
Keyword(s):  
Asymptotic Behavior ◽  
Boundary Value Problems ◽  
Reaction Diffusion ◽  
Initial Boundary ◽  
Reaction Diffusion Equations ◽  
Singularly Perturbed ◽  
Diffusion Equations ◽  
Initial Boundary Value Problems ◽  
Asymptotic Behavior Of Solution ◽  
Initial Boundary Value

Metastable travelling-wave solutions of singularly-perturbed reaction-diffusion equations

1998 ◽  
Vol 9 (4) ◽  
pp. 397-416 ◽  
Author(s):  
JACQUES G. L. LAFORGUE ◽  
ROBERT E. O'MALLEY ◽  
MICHAEL J. WARD
Keyword(s):  
Reaction Diffusion ◽  
Initial Boundary ◽  
Travelling Wave ◽  
Reaction Diffusion Equations ◽  
Singularly Perturbed ◽  
Diffusion Equations ◽  
Time Interval ◽  
Long Time ◽  
Spatial Domains ◽  
Initial Boundary Value

This paper determines the asymptotic solution of certain initial-boundary value problems for singularly-perturbed reaction-diffusion equations, including the Allen–Cahn and Cahn–Hilliard equations, on bounded one-dimensional spatial domains for r[ges ]0. Attention is focused on the metastable evolution of a transition layer over an asymptotically exponentially-long time interval.

Asymptotic estimates of solutions to initial-boundary-value problems for distributed order time-fractional diffusion equations

2014 ◽  
Vol 17 (4) ◽  
Author(s):  
Zhiyuan Li ◽  
Yuri Luchko ◽  
Masahiro Yamamoto
Keyword(s):  
Asymptotic Behavior ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Initial Boundary ◽  
Fractional Diffusion ◽  
Diffusion Equations ◽  
Initial Boundary Value Problems ◽  
Fractional Diffusion Equations ◽  
Initial Boundary Value ◽  
Distributed Order

AbstractThis article deals with investigation of some important properties of solutions to initial-boundary-value problems for distributed order time-fractional diffusion equations in bounded multi-dimensional domains. In particular, we investigate the asymptotic behavior of the solutions as the time variable t → 0 and t → +∞. By the Laplace transform method, we show that the solutions decay logarithmically as t → +∞. As t → 0, the decay rate of the solutions is dominated by the term (t log(1/t))−1. Thus the asymptotic behavior of solutions to the initial-boundary-value problem for the distributed order time-fractional diffusion equations is shown to be different compared to the case of the multi-term fractional diffusion equations.

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