Asymptotic Behavior of Solutions of Evolution Equations and the Construction of Holomorphic Retractions

1998 ◽  
Vol 189 (1) ◽  
pp. 171-178 ◽  
Author(s):  
Victor Khatskevich ◽  
Simeon Reich ◽  
David Shoikhet
Keyword(s):  
Asymptotic Behavior ◽  
Evolution Equations ◽  
Asymptotic Behavior Of Solutions

scholarly journals Asymptotic behavior of solutions for a semibounded nonmonotone evolution equation

2003 ◽  
Vol 2003 (9) ◽  
pp. 521-538
Author(s):  
Nikos Karachalios ◽  
Nikos Stavrakakis ◽  
Pavlos Xanthopoulos
Keyword(s):  
Dynamical System ◽  
Asymptotic Behavior ◽  
Parabolic Equation ◽  
Evolution Equation ◽  
Existence And Uniqueness ◽  
Nonlinear Parabolic Equation ◽  
Evolution Equations ◽  
Asymptotic Behavior Of Solutions ◽  
Uniqueness Of Solutions ◽  
Nonlinear Parabolic

We consider a nonlinear parabolic equation involving nonmonotone diffusion. Existence and uniqueness of solutions are obtained, employing methods for semibounded evolution equations. Also shown is the existence of a global attractor for the corresponding dynamical system.

scholarly journals Random time change and related evolution equations. Time asymptotic behavior

2019 ◽  
Vol 20 (05) ◽  
pp. 2050034
Author(s):  
Anatoly N. Kochubei ◽  
Yuri G. Kondratiev ◽  
José L. da Silva
Keyword(s):  
Asymptotic Behavior ◽  
Asymptotic Analysis ◽  
Evolution Equations ◽  
Random Time ◽  
Asymptotic Behavior Of Solutions ◽  
Kolmogorov Equations ◽  
Random Time Change ◽  
Time Changes ◽  
Random Times ◽  
Time Asymptotic Behavior

In this paper, we investigate the time asymptotic behavior of solutions to fractional in time evolution equations which appear as results of random time changes in Markov processes. We consider inverse subordinators as random times and use the subordination principle for the solutions to forward Kolmogorov equations. The classes of subordinators for which asymptotic analysis may be realized are described.

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