相关论文: Attractors for nonlinear reaction-diffusion system…

We consider a diffusion on a bounded domain, assuming that the system is irreducible inside the domain and that the diffusion has varying degree of degeneracy on the domain's boundary. The long-term statistical properties of typical…

We investigate the long term behavior in terms of global attractors, as time goes to infinity, of solutions to a continuum model for biological aggregations in which individuals experience long-range social attraction and short range…

We show that for any fixed accuracy and time length $T$, a {\it finite} number of $T$-time length pieces of the complete trajectories on the global attractor are capable of uniformly approximating all trajectories within the accuracy in the…

In this paper we study the long-time behavior of a nonlocal Cahn-Hilliard system with singular potential, degenerate mobility, and a reaction term. In particular, we prove the existence of a global attractor with finite fractal dimension,…

We give a comprehensive study of the analytic properties and long-time behavior of solutions of a reaction-diffusion system in a bounded domain in the case where the nonlinearity satisfies the standard monotonicity assumption. We pay the…

In this paper we prove the existence of a trajectory attractor (in the sense of V.V. Chepyzhov and M.I. Vishik) for a nonlinear PDE system coming from a 3D liquid crystal model accounting for stretching effects. The system couples a…

The long-time asymptotics is analyzed for all finite energy solutions to a model U(1)-invariant nonlinear Klein-Gordon equation in one dimension, with the nonlinearity concentrated at a single point: each finite energy solution converges as…

This work deals with a parabolic chemotaxis model with nonlinear diffusion and nonlocal reaction source. The problem is formulated on the whole space and, depending on a specific interplay between the coefficients associated to such…

We prove existence of global attractors for parabolic equations of the form $$u_t+\beta(x)u-\sum_{ij}\partial_i(a_{ij}(x)\partial_j u)=f(x,u)$$ with Dirichlet boundary condition on an arbitrary unbounded domain $\Omega$ in $\R^3$, without…

Consider classical solutions to the parabolic reaction diffusion equation $$ &u_t =Lu+f(x,u), (x,t)\in R^n\times(0,\infty); &u(x,0) =g(x)\ge0, x\in R^n; &u\ge0, $$ where $$ L=\sum_{i,j=1}^na_{i,j}(x)\frac{\partial^2}{\partial x_i \partial…

We consider an initial boundary value problem for a quantum version of the Zakharov system arising in plasma physics. We prove the global well-posedness of this problem in some Sobolev type classes and study properties of solutions. This…

The Cahn-Hilliard-Navier-Stokes system is based on a well-known diffuse interface model and describes the evolution of an incompressible isothermal mixture of binary fluids. A nonlocal variant consists of the Navier-Stokes equations…

Under consideration is the hyperbolic relaxation of a semilinear reaction-diffusion equation on a bounded domain, subject to a dynamic boundary condition. We also consider the limit parabolic problem with the same dynamic boundary…

We consider the Neumann and Cauchy problems for positivity preserving reaction-diffusion systems of $m$ equations enjoying the mass and entropy dissipation properties. We show global classical existence in any space dimension, under the…

Second initial boundary problem in narrow domains of width $\epsilon\ll 1$ for linear second order differential equations with nonlinear boundary conditions is considered in this paper. Using probabilistic methods we show that the solution…

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…

The existence of a global attractor for wave equations in unbounded domains is a challenging problem due to the non-compactness of the Sobolev embeddings. To overcome this difficulty, some authors have worked with weighted Sobolev spaces…

We obtain the existence and the structure of the weak uniform (with respect to the initial time) global attractor and construct a trajectory attractor for the 3D Navier-Stokes equations (NSE) with a fixed time-dependent force satisfying a…

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…

We consider the subcritical SQG equation in its natural scale invariant Sobolev space and prove the existence of a global attractor of optimal regularity. The proof is based on a new energy estimate in Sobolev spaces to bootstrap the…