Related papers: Pullback attractors for a singularly nonautonomous…
In this article we study the asymptotic behavior of solutions, in sense of global pullback attractors, of the evolution system $$ \begin{cases} u_{tt} +\eta\Delta^2 u+a(t)\Delta\theta=f(t,u), & t>\tau,\ x\in\Omega,\\ \theta_t-\kappa\Delta…
The aim of this paper is to study the robustness of the family of pullback attractors associated to a non-autonomous coupled system of strongly damped wave equations, given by the following evolution system $$\left\{ \begin{array}{lr}…
The purpose of this paper is to give a characterization of the structure of non-autonomous attractors of the problem $u_t= u_{xx} + \lambda u - \beta(t)u^3$ when the parameter $\lambda > 0$ varies. Also, we answer a question proposed in…
Consider the family of semilinear parabolic problems \begin{equation*} \left\{ \begin{array}{lll} u_{t}(x,t) = \Delta u(x,t) - au(x,t) + f(u(x,t)), \,\,\, x \in \Omega_{\epsilon}, t > 0, \\ \frac{\partial u}{\partial N} (x,t) = g(u(x,t)),…
In this work we consider the non local evolution equation with time-dependent terms which arises in models of phase separation in $\mathbb{R}^N$ \[ \partial_t u=- u + g \left(\beta(J*u) +\beta h(t,u)\right) \] under some restrictions on…
Under consideration is the damped semilinear wave equation \[ u_{tt}+u_t-\Delta u + u + f(u)=0 \] on a bounded domain $\Omega$ in $\mathbb{R}^3$ with a perturbation parameter $\varepsilon>0$ occurring in an acoustic boundary condition,…
Under consideration is the damped semilinear wave equation \[ u_{tt}+u_t-\Delta u+u+f(u)=0 \] in a bounded domain $\Omega$ in $\mathbb{R}^3$ subject to an acoustic boundary condition with a singular perturbation, which we term "massless…
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…
The aim of this paper is to analyze the long-time dynamical behavior of the solution for a degenerate wave equation with time-dependent damping term $\partial_{tt}u + \beta(t)\partial_tu = \mathcal{L}u(x,t) + f(u)$ on a bounded domain…
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…
In this paper, we mainly study the regularity of pullback $\mathcal{D}$-attractors for a nonautonomous nonclassical diffusion equation with delay term $b(t,u_t)$ which contains some hereditary characteristics. Under a critical nonlinearity…
We investigate the initial-value problem for the semilinear plate equation containing localized strong damping, localized weak damping and nonlocal nonlinearity. We prove that if nonnegative damping coefficients are strictly positive almost…
The paper investigates the existence of global attractors and their upper semicontinuity for a structural damped wave equation on $\mathbb{R}^{N}: u_{tt}-\Delta u+(-\Delta)^\alpha u_{t}+u_{t}+u+g(u)=f(x)$, where $\alpha\in (1/2, 1)$ is…
This work investigates the semilinear wave equation featuring the displacement dependent term $\sigma(u)\partial_t u $ and nonlinearity $f(u)$. By developing refined space-time a priori estimates under extended ranges of the nonlinearity…
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…
The paper investigates the existence and upper semicontinuity of uniform attractors of the perturbed non-autonomous Kirchhoff wave equations with strong damping and supercritical nonlinearity: $u_{tt}-\Delta u_{t}-(1+\epsilon\|\nabla…
We prove existence of global attractors for damped hyperbolic equations of the form $$\aligned \eps u_{tt}+\alpha(x) u_t+\beta(x)u- \sum_{ij}(a_{ij}(x) u_{x_j})_{x_i}&=f(x,u),\quad x\in \Omega, t\in[0,\infty[, u(x,t)&=0,\quad x\in \partial…
We consider a family of semilinear parabolic problems with nonlinear boundary conditions \[ \left\{ \begin{aligned} u_t(x,t) &=\Delta u(x,t) -au(x,t) + f(u(x,t)),\ x \in \Omega_\epsilon \mbox{ and } t>0\,,\\ \displaystyle\frac{\partial…
We present a new method of investigating the so-called quasi-linear strongly damped wave equations $$ \partial_t^2u-\gamma\partial_t\Delta_x u-\Delta_x u+f(u)= \nabla_x\cdot \phi'(\nabla_x u)+g $$ in bounded 3D domains. This method allows…
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…