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This paper is concerned with pullback attractors of the stochastic p-Laplace equation defined on the entire space R^n. We first establish the asymptotic compactness of the equation in L^2(R^n) and then prove the existence and uniqueness of…

Analysis of PDEs · Mathematics 2014-09-30 Andrew Krause , Bixiang Wang

In this paper, a standard about the existence and upper semi-continuity of pullback attractors in the non-initial space is established for some classes of non-autonomous SPDE. This pullback attractor, which is the omega-limit set of the…

Analysis of PDEs · Mathematics 2015-04-17 Wenqiang Zhao , Shuzhi Song

New results on the behaviour of the fast motion in slow-fast systems of ODEs with dependence on the fast time are given in terms of tracking of nonautonomous attractors. Under quite general assumptions, including the uniform ultimate…

Dynamical Systems · Mathematics 2024-06-24 Iacopo P. Longo , Rafael Obaya , Ana M. Sanz

We study the non-autonomous weakly damped wave equation with subquintic growth condition on the nonlinearity. Our main focus is the class of Shatah--Struwe solutions, which satisfy the Strichartz estimates and are coincide with the class of…

Analysis of PDEs · Mathematics 2021-01-19 Jakub Banaśkiewicz , Piotr Kalita

In this work we study a dissipative one dimensional scalar parabolic problem with non-local nonlinear diffusion with delay. We consider the general situation in which the functions involved are only continuous and solutions may not be…

Analysis of PDEs · Mathematics 2025-06-11 Tomás Caraballo , A. N. Carvalho , Yessica Julio

We study pullback attractors of non-autonomous non-compact dynamical systems generated by differential equations with non-autonomous deterministic as well as stochastic forcing terms. We first introduce the concepts of pullback attractors…

Analysis of PDEs · Mathematics 2012-04-24 Bixiang Wang

In this paper, we study the strong global attractors for a three dimensional nonclassical diffusion equation with memory. First, we prove the existence and uniqueness of strong solutions for the equations by the Galerkin method. Then we…

Analysis of PDEs · Mathematics 2023-04-03 Yuming Qin , Xiaolei Dong , Alain Miranville , Ke Wang

As it is well-known, the forwards and pullback dynamics are in general unrelated. In this paper we present an in-depth study of whether the pullback attractor is also a forwards attractor for the processes involved with the skew-product…

Dynamical Systems · Mathematics 2020-08-26 José antonio langa , Rafael Obaya , Ana María Sanz

In this paper, we investigate the continuity of the attractors in time-dependent phase spaces. (i) We establish two abstract criteria on the upper semicontinuity and the residual continuity of the pullback $\mathscr D$-attractor with…

Analysis of PDEs · Mathematics 2022-01-11 Yanan Li , Zhijian Yang

This study investigates a semilinear wave equation characterized by nonlinear damping $g(u_t) $ and nonlinearity $f(u)$. First, the well-posedness of weak solutions across broader exponent ranges for $g$ and $f$ is established, by utilizing…

Analysis of PDEs · Mathematics 2025-02-14 Cuncai Liu , Fengjuan Meng , Xiaoying Han , Chang Zhang

This paper concerns the tempered pullback dynamics of 2D incompressible non-autonomous Navier-Stokes equation with non-homogeneous boundary condition on Lipschitz-like domain. With the presence of a time-dependent external force f(t) which…

Analysis of PDEs · Mathematics 2018-04-24 Xin-Guang Yang , Yuming Qin , To Fu Ma , Yongjin Lu

We are interested in studying a non-autonomous semilinear heat equation with homogeneous Neumann boundary conditions on time-varying domains. Using a differential geometry approach with coordinate transformations technique, we will show…

Analysis of PDEs · Mathematics 2025-07-01 Gleiciane S. Aragão , Flank D. M. Bezerra , Lucas G. Mendonça

This article discusses the weak pullback attractors for a damped stochastic fractional Schr\"odinger equation on $\mathbb{R}^n$ with $n\geq 2$. By utilizing the stochastic Strichartz estimates and a stopping time technique argument, the…

Analysis of PDEs · Mathematics 2024-11-06 Ao Zhang , Yanjie Zhang , Sanyang Zhai , Li Lin

We consider dynamical behavior of non-autonomous wave-type evolutionary equations with nonlinear damping, critical nonlinearity, and time-dependent external forcing which is translation bounded but not translation compact (i.e., external…

Dynamical Systems · Mathematics 2009-11-11 Chunyou Sun , Daomin Cao , Jinqiao Duan

We study long-time dynamics of a class of abstract second order in time evolution equations in a Hilbert space with the damping term depending both on displacement and velocity. This damping represents the nonlinear strong dissipation…

Dynamical Systems · Mathematics 2010-10-26 Igor Chueshov , Stanislav Kolbasin

This paper is devoted to initial-boundary value problem of an extensible beam equation with degenerate nonlocal energy damping in $\Omega\subset\mathbb{R}^n$: $u_{tt}-\kappa\Delta u+\Delta^2u-\gamma(\Vert \Delta u\Vert^2+\Vert…

Analysis of PDEs · Mathematics 2023-04-28 Senlin Yan , Chengkui Zhong

We examine a viscous Cahn-Hilliard phase-separation model with memory and where the chemical potential possesses a nonlocal fractional Laplacian operator. The existence of global weak solutions is proven using a Galerkin approximation…

Analysis of PDEs · Mathematics 2018-05-01 Eylem Öztürk , Joseph L. Shomberg

In this paper, we study the structure of the global attractor for weak and regular solutions of a problem governed by a scalar semilinear reaction-diffusion equation with a non-regular nonlinearity, such that uniquness of solutions can fail…

Analysis of PDEs · Mathematics 2026-03-02 Rubén Caballero , Piotr Kalita , José Valero

The existence of a pullback attractor is established for the singularly perturbed FitzHugh-Nagumo system defined on the entire space $R^n$ when external terms are unbounded in a phase space. The pullback asymptotic compactness of the system…

Analysis of PDEs · Mathematics 2008-05-27 Bixiang Wang

We study the asymptotic dynamics of stochastic Young differential delay equations under the regular assumptions on Lipschitz continuity of the coefficient functions. Our main results show that, if there is a linear part in the drift term…

Dynamical Systems · Mathematics 2020-07-31 Nguyen Dinh Cong , Luu Hoang Duc , Phan Thanh Hong