Results 41 to 50 of about 309 (70)

Global attractor of the extended Fisher-Kolmogorov equation in H^k spaces

Boundary Value Problems, 2011
The long-time behavior of solution to extended Fisher-Kolmogorov equation is considered in this article. Using an iteration procedure, regularity estimates for the linear semigroups and a classical existence theorem of global attractor, we prove that the
Luo Hong
doaj  

Existence of the global attractor for the plate equation with nonlocal nonlinearity in R^{n} [PDF]

arXiv, 2015
We consider Cauchy problem for the semilinear plate equation with nonlocal nonlinearity. Under mild conditions on the damping coefficient, we prove that the semigroup generated by this problem possesses a global attractor.
arxiv  

Global Attractor for the Periodic Generalized Korteweg-de Vries Equation Through Smoothing [PDF]

arXiv, 2021
We establish a smoothing result for the generalized KdV (gKdV) on the torus with polynomial non-linearity, damping, and forcing that matches the smoothing level for the gKdV at $H^1$. As a consequence, we establish the existence of a global attractor for this equation as well as its compactness in $H^s(\mathbb{T})$, $s\in (1,2).$
arxiv  

Random attractors of Kirchhoff-type reaction–diffusion equations without uniqueness driven by nonlinear colored noise

Open Mathematics
In this article, we consider the asymptotic behavior of solutions for the Kirchhoff-type reaction–diffusion equations driven by a nonlinear colored noise defined on unbounded domains. We prove the existence and uniqueness of pullback random attractors by
Zhang Zhang, Yao Xiaobin
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On a class of PDEs with nonlinear distributed in space and time state-dependent delay term [PDF]

arXiv, 2006
A new class of nonlinear partial differential equations with distributed in space and time state-dependent delay is investigated. We find appropriate assumptions on the kernel function which represents the state-dependent delay and discuss advantages of this class.
arxiv  

Attractors for the viscous Camassa-Holm equation [PDF]

arXiv, 2006
We show that the viscous Camassa-Holm equation subject to an external force, and where the viscosity term is given by second order differential operator in divergence form has a global attractors in the energy space $H^1$. Moreover, we establish an asymptotic smoothing effect.
arxiv  

On the Domain of Analyticity and Small Scales for the Solutions of the Damped-driven 2D Navier-Stokes Equations [PDF]

arXiv, 2007
We obtain a logarithmically sharp estimate for the space-analyticity radius of the solutions of the damped-driven 2D Navier-Stokes equations with periodic boundary conditions and relate this to the small scales in this system. This system is inspired by the Stommel--Charney barotropic ocean circulation model.
arxiv  

Partial Inertial Manifolds for infinite-dimensional dynamical systems: Example for P.D.E.s with a state-dependent delay [PDF]

arXiv, 2007
We propose a new notion of Partial Inertial Manifold to study the long-time asymptotic behavior of dissipative differential equations. As shown on an example, such manifolds may exist in the cases when the classical Inertial manifold does not exist (or not known to exist).
arxiv  

Asymptotic behaviour of the non-autonomous 3D Navier-Stokes problem with coercive force [PDF]

, 2010
We construct pullback attractors to the weak solutions of the three-dimensional Dirichlet problem for the incompressible Navier-Stokes equations in the case when the external force may become unbounded as time goes to plus or minus infinity.
arxiv   +1 more source

Dynamics for wave equations connected in parallel with nonlinear localized damping

Advances in Nonlinear Analysis
This study investigates the properties of solutions about one-dimensional wave equations connected in parallel under the effect of two nonlinear localized frictional damping mechanisms.
Gao Yunlong, Sun Chunyou, Zhang Kaibin
doaj   +1 more source