共查询到20条相似文献,搜索用时 31 毫秒
1.
Benedetta Ferrario 《随机分析与应用》2013,31(2):379-407
Abstract For the one-dimensional Kuramoto–Sivashinsky equation with random forcing term, existence and uniqueness of solutions is proved. Then, the Markovian semigroup is well defined; its properties are analyzed in order to provide sufficient conditions for existence and uniqueness of invariant measures for this stochastic equation. Finally, regularity results are presented. 相似文献
2.
本文考虑带小扰动的随机发展方程,证明如何建立此方程的耦合解.作为应用,我们证明解的Feller连续性和不变测度的存在唯一性.还进一步建立了当扰动趋于零时,关于这族不变测度的大偏差原理. 相似文献
3.
Fu Bao Xi 《数学学报(英文版)》2001,17(4):631-642
In this paper we consider a random evolution equation with small perturbations, and show how to construct coupled solutions
to the equations. As applications, we prove the Feller continuity of the solutions and the existence and uniqueness of invariant
measures. Furthermore, we establish a large deviations principle for the family of invariant measures as the perturbations
tend to zero.
Received March 20,1998, Accepted June 1, 2000 相似文献
4.
Xicheng Zhang 《Bulletin des Sciences Mathématiques》2007,131(2):175-217
By solving a deterministic Skorohod problem in the framework of evolutional triple, we prove the existence and uniqueness of solutions to multivalued stochastic evolution equations involving maximal monotone operators. The existence and uniqueness of invariant measures associated with the solutions as Markov processes are also considered in the present paper. Moreover, we apply the results to stochastic differential equations with normal reflecting boundary conditions and with singular drift terms, as well as a class of multivalued nonlinear stochastic partial differential equations with possibly discontinuous coefficients. 相似文献
5.
Sergio Albeverio Zdzis?aw Brze?niak 《Journal of Mathematical Analysis and Applications》2010,371(1):309-322
The purpose of this paper is twofold. Firstly, we investigate the problem of existence and uniqueness of solutions to stochastic differential equations with one sided dissipative drift driven by semi-martingales. Secondly, we investigate the problem of existence of an invariant measure for such equations when the coefficients are time independent. 相似文献
6.
Jong Uhn Kim 《Applied Mathematics and Optimization》2008,58(1):29-67
We discuss an initial boundary value problem for the stochastic wave equation with nonlinear damping. We establish the existence
and uniqueness of a solution. Our method for the existence of pathwise solutions consists of regularization of the equation
and data, the Galerkin approximation and an elementary measure-theoretic argument. We also prove the existence of an invariant
measure when the equation has pure nonlinear damping. 相似文献
7.
In this paper, we proved the global existence and uniqueness of the strong, weak and mild solutions for one-dimensional Burgers equation perturbed by a Poisson form process, a Poisson form and Q-Wiener process with the Dirichlet bounded condition. We also proved the existence of the invariant measure of these models. 相似文献
8.
Some recent developments in the analysis of long-time behaviors of
stochastic solutions of nonlinear conservation laws driven by
stochastic forcing are surveyed. The existence and uniqueness of
invariant measures are established for anisotropic degenerate
parabolic-hyperbolic conservation laws of second-order driven by
white noises. Some further developments, problems, and challenges in
this direction are also discussed. 相似文献
9.
Lagerstrom's model problem is a classical singular perturbation problem which was introduced to illustrate the ideas and subtleties involved in the analysis of viscous flow past a solid at low Reynolds number by the method of matched asymptotic expansions. In this paper the corresponding boundary value problem is analyzed geometrically by using methods from the theory of dynamical systems, in particular invariant manifold theory. As an essential part of the dynamics takes place near a line of non-hyperbolic equilibria, a blow-up transformation is introduced to resolve these singularities. This approach leads to a constructive proof of existence and local uniqueness of solutions and to a better understanding of the singular perturbation nature of the problem. In particular, the source of the logarithmic switchback phenomenon is identified. 相似文献
10.
In this paper, we consider the ergodicity of invariant measures for the stochastic Ginzburg-Landau equation with degenerate random forcing. First, we show the existence and pathwise uniqueness of strong solutions with H1-initial data, and then the existence of an invariant measure for the Feller semigroup by the Krylov-Bogoliubov method. Then in the case of degenerate additive noise, using the notion of asymptotically strong Feller property, we prove the uniqueness of invariant measures for the transition semigroup. 相似文献
11.
In this paper, we study the dynamics of a two-dimensional stochastic Navier-Stokes equation on a smooth domain, driven by linear multiplicative white noise. We show that solutions of the 2D Navier-Stokes equation generate a perfect and locally compacting C1,1 cocycle. Using multiplicative ergodic theory techniques, we establish the existence of a discrete non-random Lyapunov spectrum for the cocycle. The Lyapunov spectrum characterizes the asymptotics of the cocycle near an equilibrium/stationary solution. We give sufficient conditions on the parameters of the Navier-Stokes equation and the geometry of the planar domain for hyperbolicity of the zero equilibrium, uniqueness of the stationary solution (viz. ergodicity), local almost sure asymptotic stability of the cocycle, and the existence of global invariant foliations of the energy space. 相似文献
12.
《Stochastic Processes and their Applications》2020,130(8):5100-5123
This paper proves a Krylov–Safonov estimate for a multidimensional diffusion process whose diffusion coefficients are degenerate on the boundary. As applications the existence and uniqueness of invariant probability measures for the process and Hölder estimates for the associated partial differential equation are obtained. 相似文献
13.
Luigi Manca 《随机分析与应用》2013,31(2):399-426
Abstract We consider stochastic semilinear partial differential equations with Lipschitz nonlinear terms. We prove existence and uniqueness of an invariant measure and the existence of a solution for the corresponding Kolmogorov equation in the space L 2(H;ν), where ν is the invariant measure. We also prove the closability of the derivative operator and an integration by parts formula. Finally, under boundness conditions on the nonlinear term, we prove a Poincaré inequality, a logarithmic Sobolev inequality, and the ipercontractivity of the transition semigroup. 相似文献
14.
Jong Uhn Kim 《Transactions of the American Mathematical Society》2008,360(2):575-607
We prove the existence and uniqueness of solutions to the initial boundary value problem for a one-dimensional wave equation with unilateral boundary conditions and random noise. We also establish the existence of an invariant measure.
15.
Michal Feckan 《Proceedings of the American Mathematical Society》2001,129(11):3395-3399
Bendixson's condition on the nonexistence of periodic solutions for planar ordinary differential equations is extended to higher dimensional ordinary differential equations with first integrals to preclude the existence of certain invariant Lipschitz compact submanifolds for those equations.
16.
On Wiener-Poisson type multivalued stochastic differential equations with non-Lipschitz coefficients
Jing Wu 《数学学报(英文版)》2013,29(4):675-690
In this paper, we prove local uniqueness for multivalued stochastic differential equations with Poisson jumps. Then existence and uniqueness of global solutions is obtained under the conditions that the coefficients satisfy locally Lipschitz continuity and one-sided linear growth of b. Moreover, we also prove the Markov property of the solution and the existence of invariant measures for the corresponding transition semigroup. 相似文献
17.
In this paper, we consider the existence of positive, negative and sign-changing solutions for some fourth order semilinear elliptic boundary value problems. We present new results on invariant sets of the gradient flows of the corresponding variational functionals. The structure of the invariant sets will be built into minimax procedures to construct the sign-changing solutions. 相似文献
18.
Bifurcations of Invariant Tori and Subharmonic Solutions of Singularly Perturbed System 总被引:1,自引:1,他引:0
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This paper deals with bifurcations of subharmonic solutions and invariant tori generated from limit cycles in the fast dynamics for a nonautonomous singularly perturbed system. Based on Poincare map, a series of blow-up transformations and the theory of integral manifold, the conditions for the existence of invariant tori are obtained, and the saddle-node bifurcations of subharmonic solutions are studied. 相似文献
19.
Bixiang Wang 《随机分析与应用》2020,38(2):213-237
AbstractWe study the random dynamics of the N-dimensional stochastic Schrödinger lattice systems with locally Lipschitz diffusion terms driven by locally Lipschitz nonlinear noise. We first prove the existence and uniqueness of solutions and define a mean random dynamical system associated with the solution operators. We then establish the existence and uniqueness of weak pullback random attractors in a Bochner space. We finally prove the existence of invariant measures of the stochastic equation in the space of complex-valued square-summable sequences. The tightness of a family of probability distributions of solutions is derived by the uniform estimates on the tails of the solutions at far field. 相似文献
20.
Some results on the invariant regions ,existence and uniqueness of solutions to a class of integrodifferential systems are established. Applying these results to integrodifferential systems with a small parameter ε > 0, we obtain,in particular, some estimates of solutions uniform in ε > 0. 相似文献