ASYMPTOTICS FOR LARGE TIME OF SOLUTIONS OF A SYSTEM OF EQUATIONS FOR SURFACE WAVES

1992 ◽  
Vol 38 (3) ◽  
pp. 525-551
Author(s):  
P I Naumkin ◽  
I A Shishmarëv
Keyword(s):  
Surface Waves ◽  
Large Time ◽  
System Of Equations ◽  
Asymptotics For Large Time

scholarly journals Asymptotic and transient behaviour for a nonlocal problem arising in population genetics

2018 ◽  
Vol 31 (1) ◽  
pp. 84-110
Author(s):  
J.-B. BURIE ◽  
R. DJIDJOU-DEMASSE ◽  
A. DUCROT
Keyword(s):  
Asymptotic Behaviour ◽  
Large Time ◽  
Nonlocal Problem ◽  
Genetic Adaptation ◽  
System Of Equations ◽  
Pathogen Population ◽  
Transient Behaviour ◽  
Selection Processes ◽  
The One ◽  
Mutation And Selection

This work is devoted to the study of an integro-differential system of equations modelling the genetic adaptation of a pathogen by taking into account both mutation and selection processes. First, we study the asymptotic behaviour of the system and prove that it eventually converges to a stationary state. Next, we more closely investigate the behaviour of the system in the presence of multiple EAs. Under suitable assumptions and based on a small mutation variance asymptotic, we describe the existence of a long transient regime during which the pathogen population remains far from its asymptotic behaviour and highly concentrated around some phenotypic value that is different from the one described by its asymptotic behaviour. In that setting, the time needed for the system to reach its large time configuration is very long and multiple evolutionary attractors may act as a barrier of evolution that can be very long to bypass.

Excitation of surface waves in magnetohydrodynamics

1990 ◽  
Vol 43 (2) ◽  
pp. 183-188 ◽  
Author(s):  
Bhimsen K. Shivamoggi
Keyword(s):  
Magnetic Field ◽  
Gravitational Field ◽  
Asymptotic Behaviour ◽  
Pressure Distribution ◽  
Surface Waves ◽  
Initial Value Problem ◽  
Large Time ◽  
Far Field ◽  
Two Dimensional ◽  
Initial Value

A study is made of the transient development of two-dimensional linearized surface waves generated by a localized steady pressure distribution on the interface between a uniformly streaming, semi-infinite, infinitely conducting plasma subjected to a gravitational field and the confining vacuum magnetic field. The linearized equations associated with an initial-value problem are used to obtain the large-time asymptotic behaviour of the disturbance in the far field.

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