Institutul de Matematică şi Informatică "Vladimir Andrunachievici"
Universitatea de Stat din MoldovaRO EN
The comparability of motions in dynamical systems and recurrent solutions of (S)PDEs
Authors: David Cheban and Zhenxin Liu
Keywords: comparability, recurrent motions, uniform space, infinite-dimensional differential equations
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Keywords: comparability, recurrent motions, uniform space, infinite-dimensional differential equations
Abstract
Shcherbakov's comparability method is very useful to study recurrent solutions of differential equations. In this paper, we extend the method from metric spaces to uniform spaces, which applies well to dynamical systems in infinite-dimensional spaces. This generalized comparability method can be easily used to study recurrent solutions of (stochastic) partial differential equations under weaker conditions than in earlier results. We also show that the distribution of solutions of SDEs naturally generates a semiflow or skew-product semiflow on the space of probability measures, which is interesting in itself. As illustration, we give an application to semilinear stochastic partial differential equations.David Cheban
State University of Moldova, Faculty of Mathematics and
Informatics, Department of Mathematics, A. Mateevich
Street 60, MD–2009 Chisinau, Moldova
E-mail: ,
Zhenxin Liu (Corresponding author)
School of Mathematical Sciences, Dalian University of
Technology, Dalian 116024, P. R. China
E-mail:
State University of Moldova, Faculty of Mathematics and
Informatics, Department of Mathematics, A. Mateevich
Street 60, MD–2009 Chisinau, Moldova
E-mail: ,
Zhenxin Liu (Corresponding author)
School of Mathematical Sciences, Dalian University of
Technology, Dalian 116024, P. R. China
E-mail:
DOI
https://doi.org/10.56415/basm.y2024.i1-2.p53Fulltext
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Contents
- Professor Boris Șcerbacov - 100th anniversary
- Metrically piecewise continuous p-almost periodic functions and applications
- Poisson Stable Solutions of Semi-Linear Differential Equations
- Asymptotic behaviour of non-autonomous Caputo fractional differential equations with a one-sided dissipative vector field
- The comparability of motions in dynamical systems and recurrent solutions of (S)PDEs
- The family of cubic differential systems with two real and two complex distinct infinite singularities and invariant straight lines of the type (2,2,2)
- On the attractors of weakly hyperbolic IFS's with condensation
- An optimality criterion for disjoint bilinear programming and its application to the problem with an acute-angled polytope for a disjoint subset
- Completeness of the factor group of a complete topological Abelian group by a discrete subgroup
- Remembering Professor B. A. Shcherbakov (1924-2017)
