Related papers: Existence and regularity of pullback attractors fo…

We investigate the late-time asymptotic solutions and attractor structure of the spin density in minimal causal spin hydrodynamics in Gubser flow. After deriving the differential equation governing the spin density, we obtain its late-time…

A long-time behavior of solutions to a nonlinear plate model subject to non-conservative and non-dissipative effects and nonlinear damping is considered. The model under study is a prototype for a suspension bridge under the effects of…

In this paper, we first prove an abstract theorem on the existence of polynomial attractors and the concrete estimate of their attractive velocity for infinite-dimensional dynamical systems, then apply this theorem to a class of wave…

We demonstrate that standard delay systems with a linear instantaneous and a delayed nonlinear term show weak chaos, asymptotically subdiffusive behavior, and weak ergodicity breaking if the nonlinearity is chosen from a specific class of…

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…

Chemical and biochemical reactions can exhibit surprisingly different behaviours, ranging from multiple steady-state solutions to oscillatory solutions and chaotic behaviours. These types of systems are often modelled by a system of…

We address the global-in-time existence, stability and long time behaviour of weak solutions of the three-dimensional compressible Navier-Stokes equations with potential force. We show the details of the $\alpha$-dependence of different…

We study the well-posedness, steady states and long time behavior of solutions to Vlasov-Fokker-Planck equation with external confinement potential and nonlinear self-consistent interactions. Our analysis introduces newly characterized…

We give an abstract framework for studying nonautonomous PDEs, called a generalized evolutionary system. In this setting, we define the notion of a pullback attractor. Moreover, we show that the pullback attractor, in the weak sense, must…

We study differential equations with a linear, path dependent drift and discrete delay in the diffusion term driven by a $\gamma$-H\"older rough path for $\gamma > \frac{1}{3}$. We prove well-posedness of these systems and establish a…

We present a complete description of the similarity solutions $u_{\alpha}(x,t)=t^{-\alpha/2}f(\Vert x \Vert/\sqrt{t};\alpha)$ for the following nonlinear diffusion equation $$ u_{t}+\gamma\vert u_{t} \vert =\Delta u\qquad(-1<\gamma<1) $$…

In the present paper, we study the Cauchy-Dirichlet problem to the nonlocal nonlinear diffusion equation with polynomial nonlinearities $$\mathcal{D}_{0|t}^{\alpha…

We address, in a three-dimensional spatial setting, both the viscous and the standard Cahn-Hilliard equation with a nonconstant mobility coefficient. As it was shown in J.W. Barrett and J.W. Blowey, Math. Comp., 68 (1999), 487-517, one…

This paper concerns the nonautonomous reaction-diffusion equation \[ u_t=u_{xx}+ug(t,x-ct,u), \quad t>0,x\in\mathbb{R}, \] where $c\in\mathbb{R}$ is the shifting speed, and the time periodic nonlinearity $ug(t,\xi,u)$ is asymptotically of…

In this paper, the strong existence and uniqueness for a degenerate finite system of quantile-dependent McKean-Vlasov stochastic differential equations are obtained under a weak H\"{o}rmander condition. The approach relies on the apriori…

We consider a system of several nonlinear equations with a distributed delay and obtain absolute asymptotic stability conditions, independent of the delay. The ideas of the proofs are based on the notion of a strong attractor. The results…

In this paper, we investigate the existence and uniqueness of weak pullback mean random attractors for abstract stochastic evolution equations with general diffusion terms in Bochner spaces. As applications, the existence and uniqueness of…

We study some non-parabolic diffusion problems in one-space dimension, where the diffusion flux exhibits forward and backward nature of the Perona-Malik, H\"ollig or non-Fourier type. Classical weak solutions to such problems are…

The work deals with a study of a nonlinear parabolic equation with hysteresis, containing a nonlinear monotone operator in the diffusion term. The well-posedness of the model equation is addressed by using an implicit time discretization…

We study the Cahn-Hilliard equation with non-degenerate concentration-dependent mobility and logarithmic potential in two dimensions. We show that any weak solution is unique, exhibits propagation of uniform-in-time regularity, and…