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Renhai Wang

Bio: Renhai Wang is an academic researcher from Southwest University. The author has contributed to research in topics: Mathematics & Nonlinear system. The author has an hindex of 6, co-authored 12 publications receiving 131 citations.

Papers
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Journal ArticleDOI
TL;DR: In this paper, the pullback random attractors for fractional non-classical diffusion equations driven by colored noise are established for the equations with a wide class of nonlinear diffusion terms.
Abstract: The random dynamics in \begin{document}$ H^s(\mathbb{R}^n) $\end{document} with \begin{document}$ s\in (0,1) $\end{document} is investigated for the fractional nonclassical diffusion equations driven by colored noise. Both existence and uniqueness of pullback random attractors are established for the equations with a wide class of nonlinear diffusion terms. In the case of additive noise, the upper semi-continuity of these attractors is proved as the correlation time of the colored noise approaches zero. The methods of uniform tail-estimate and spectral decomposition are employed to obtain the pullback asymptotic compactness of the solutions in order to overcome the non-compactness of the Sobolev embedding on an unbounded domain.

66 citations

Journal ArticleDOI
TL;DR: In this article, the existence and uniqueness of mean square solutions to the equations are proved when the nonlinear drift and diffusion terms are locally Lipschitz continuous and it is shown that the mean random dynamical system generated by the solution operators has a unique tempered weak pullback random attractor in a Bochner space.

31 citations

Journal ArticleDOI
TL;DR: In this paper, a bi-spatial attractor is obtained when the non-initial space is $p$-times Lebesgue space or Sobolev space, which leads to the measurability of the attractor in both state spaces.
Abstract: This paper is concerned with the regular random dynamics for the reaction-diffusion equation defined on a thin domain and perturbed by rough noise, where the usual Winner process is replaced by a general stochastic process satisfied the basic convergence. A bi-spatial attractor is obtained when the non-initial space is $p$-times Lebesgue space or Sobolev space. The measurability of the solution operator is proved, which leads to the measurability of the attractor in both state spaces. Finally, the upper semi-continuity of attractors under the $p$-norm is established when the narrow domain degenerates onto a lower dimensional set. Both methods of symbolical truncation and spectral decomposition provide all required uniform estimates in both Lebesgue and Sobolev spaces.

26 citations

Journal ArticleDOI
TL;DR: In this paper, the existence and uniqueness of tempered pullback random attractors are proved for systems defined on (n + 1 ) − dimensional unbounded narrow domains, and the upper semicontinuity of these attractors is established when a family of ( n + 1 − dimensional) unbounded thin domains collapses onto an n−dimensional unbounded domain.

20 citations


Cited by
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Book ChapterDOI
31 Oct 2006

1,424 citations

Journal ArticleDOI
TL;DR: In this article, the authors established backward compactness of a pullback random attractor (PRA) from a backward limit-set compact cocycle, which is a necessary and sufficient condition such that its time-fibers are upper semi-continuous at negative infinity.

40 citations

Journal ArticleDOI
TL;DR: In this paper, an initial value problem for a system of nonlinear parabolic pseudo equations with Caputo fractional derivatives is studied, where the continuity of the Mittag-Leffler function is related to a fractional order derivative.
Abstract: In this work, we study an initial value problem for a system of nonlinear parabolic pseudo equations with Caputo fractional derivative Here, we discuss the continuity which is related to a fractional order derivative To overcome some of the difficulties of this problem, we need to evaluate the relevant quantities of the Mittag-Leffler function by constants independent of the derivative order Moreover, we present an example to illustrate the theory

38 citations

Journal ArticleDOI
TL;DR: The existence, uniqueness, time-semi-uniform compactness and asymptotically autonomous robustness of pullback random attractors with dispersive and viscosity dissipative terms driven by operator-type noise defined on the entire space was proved in this paper.
Abstract: This paper is concerned with the asymptotic behaviour of solutions to a class of non-autonomous stochastic nonlinear wave equations with dispersive and viscosity dissipative terms driven by operator-type noise defined on the entire space $\\mathbb {R}^n$. The existence, uniqueness, time-semi-uniform compactness and asymptotically autonomous robustness of pullback random attractors are proved in $H^1(\\mathbb {R}^n)\\times H^1(\\mathbb {R}^n)$ when the growth rate of the nonlinearity has a subcritical range, the density of the noise is suitably controllable, and the time-dependent force converges to a time-independent function in some sense. The main difficulty to establish the time-semi-uniform pullback asymptotic compactness of the solutions in $H^1(\\mathbb {R}^n)\\times H^1(\\mathbb {R}^n)$ is caused by the lack of compact Sobolev embeddings on $\\mathbb {R}^n$, as well as the weak dissipativeness of the equations is surmounted at light of the idea of uniform tail-estimates and a spectral decomposition approach. The measurability of random attractors is proved by using an argument which considers two attracting universes developed by Wang and Li (Phys. D 382: 46–57, 2018).

34 citations