Related papers: On $L^{\infty }$-estimates and the structure of th…
In this paper we study the structure of the global attractor for a reaction- di{\S}usion equation in which uniqueness of the Cauchy problem is not guarantied. We prove that the global attractor can be characterized using either the unstable…
The purpose of this paper is to investigate the existence and Hausdorff dimension as well as fractal dimension of global attractors for a delayed reaction-diffusion equation on an unbounded domain. The noncompactness of the domain causes…
In this paper, we study the structure of the global attractor for the multivalued semiflow generated by a nonlocal reaction-diffusion equation in which we cannot guarantee uniqueness of the Cauchy problem. First, we analyse the existence…
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…
The purpose of this paper is to investigate the existence and estimation of Hausdorff and fractal dimension of global attractors for a delayed reaction-diffusion equation on an unbounded domain. The noncompactness of the domain cause the…
The existence of a global attractor for the solution semiflow of the extended Brusselator system in the $L^2$ phase space is proved, which is a cubic-autocatalytic and partially reversible reaction-diffusion system with linear coupling…
We consider a nonlinear reaction-diffusion equation settled on the whole euclidean space. We prove the well-posedness of the corresponding Cauchy problem in a general functional setting, namely, when the initial datum is uniformly locally…
In this paper we obtain a detailed description of the global and cocycle attractors for the skew-product semiflows induced by the mild solutions of a family of scalar linear-dissipative parabolic problems over a minimal and uniquely ergodic…
In this paper we study a nonlocal reaction-diffusion equation in which the diffusion depends on the gradient of the solution. We prove first the existence and uniqueness of regular and strong solutions. Second, we obtain the existence of…
The aim of this paper is to describe the structure of global attractors for non-autonomous difference systems of equations with recurrent (in particular, almost periodic) coefficients. We consider a special class of this type of systems…
In this paper we obtain the existence of a weak global attractor for the three-dimensional Navier-Stokes equations, that is, a weakly compact set with an invariance property, that uniformly attracts solutions, with respect to the weak…
In this paper we obtain the existence of global attractors for the dynamical systems generated by weak solution of the three-dimensional Navier-Stokes equations with damping. We consider two cases, depending on the values of the parameters…
We establish the well-posedness of a strongly damped semilinear wave equation equipped with nonlinear hyperbolic dynamic boundary conditions. Results are carried out with the presence of a parameter distinguishing whether the underlying…
A reaction-diffusion problem with an obstacle potential is considered in a bounded domain of $\R^N$. Under the assumption that the obstacle $\K$ is a closed convex and bounded subset of $\mathbb{R}^n$ with smooth boundary or it is a closed…
We consider the semilinear reaction diffusion equation $\partial_t\phi-\nu\Delta\phi-V(x)\phi+f(\phi)=0$, $\nu>0$ in a bounded domain $\Omega\subset\mathbb{R}^N$. We assume the standard Allen-Cahn-type nonlinearity, while the potential $V$…
In this work the existence of a global attractor for the solution semiflow of the coupled two-cell Brusselator model equations is proved. A grouping estimation method and a new decomposition approach are introduced to deal with the…
A method is proposed to deal with some multivalued semiflows with weak continuity properties. An application to the reaction-diffusion problems with nonmonotone multivalued semilinear boundary condition and nonmonotone multivalued…
In this paper, we study the asymptotic behavior of the solutions of a nonautonomous differential inclusion modeling a reaction-diffusion equation with a discontinuous nonlinearity. We obtain first several properties concerning the…
We study the long time behaviour of solutions for the weakly damped forced Kawahara equation on the torus. More precisely, we prove the existence of a global attractor in $L^2$, to which as time passes all solutions draw closer. In fact, we…
In this paper, we derive optimal upper and lower bounds on the dimension of the attractor AW for scalar reaction-diffusion equations with a Wentzell (dynamic) boundary condition. We are also interested in obtaining explicit bounds about the…