共查询到20条相似文献,搜索用时 93 毫秒
1.
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
2.
Ping Zhang 《Applications of Mathematics》2006,51(4):427-466
In this paper we present some results on the global existence of weak solutions to a nonlinear variational wave equation and
some related problems. We first introduce the main tools, the L
p
Young measure theory and related compactness results, in the first section. Then we use the L
p
Young measure theory to prove the global existence of dissipative weak solutions to the asymptotic equation of the nonlinear
wave equation, and comment on its relation to Camassa-Holm equations in the second section. In the third section, we prove
the global existence of weak solutions to the original nonlinear wave equation under some restrictions on the wave speed.
In the last section, we present global existence of renormalized solutions to two-dimensional model equations of the asymptotic
equation, which is also the so-called vortex density equation arising from sup-conductivity. 相似文献
3.
Shiying Zhao 《Arkiv f?r Matematik》1992,30(1):345-365
In this paper, we prove a good-λ inequality between the nontangential maximal function and the square area integral of a subharmonic
functionu in a bounded NTA domainD inR
n
. We achieve this by showing that a weighted Riesz measure ofu is a Carleson measure, with the Carleson norm bounded by a constant independent ofu. As consequences of the good-λ inequality, we obtain McConnell-Uchiyama's inequality and an analogue of Murai-Uchiyama's
inequality for subharmonic functions inD. 相似文献
4.
We prove the existence of an invariant measure for the transition semigroup associated with a nonlinear damped stochastic wave equation in Rn of the Klein--Gordon type. The uniqueness of the invariant measure and the structure of the corresponding Kolmogorov operator are also studied. 相似文献
5.
Siegfried Carl 《Applicable analysis》2013,92(6):735-753
We prove existence results for multivalued quasilinear elliptic problems of hemivariational inequality type with measure data right-hand sides. In case of L 1-data, we study existence and enclosure behaviors of solutions by an appropriate sub-supersolution approach. The proofs of our results are based on general existence theory for multivalued pseudomonotone operators, and approximation-, truncation-, and special test function techniques. 相似文献
6.
ABSTRACT An elliptic equation with Neumann boundary conditions and unbounded drift coefficients is studied in a space L 2(? d , ν) where ν is an invariant measure. The corresponding semigroup generated by the elliptic operator is identified with the transition semigroup associated with a stochastic variational inequality. 相似文献
7.
Jean-François Bony 《偏微分方程通讯》2013,38(1):23-67
We consider the quadratically semilinear wave equation on (? d , 𝔤), d ≥ 3. The metric 𝔤 is non-trapping and approaches the Euclidean metric like ?x??ρ. Using Mourre estimates and the Kato theory of smoothness, we obtain, for ρ > 0, a Keel–Smith–Sogge type inequality for the linear equation. Thanks to this estimate, we prove long time existence for the nonlinear problem with small initial data for ρ ≥ 1. Long time existence means that, for all n > 0, the life time of the solution is a least δ?n , where δ is the size of the initial data in some appropriate Sobolev space. Moreover, for d ≥ 4 and ρ > 1, we obtain global existence for small data. 相似文献
8.
We prove existence of strong solutions of Pucci extremal equations with superlinear growth in Du and unbounded coefficients. We apply this result to establish the weak Harnack inequality for Lp-viscosity supersolutions of fully nonlinear uniformly elliptic PDEs with superlinear growth terms with respect to Du.
相似文献
9.
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
10.
R. v. Vintschger 《Probability Theory and Related Fields》1989,82(2):307-313
Summary We prove the existence of an invariant measure for processes arising from a perturbation of theC[0,1]-valued Ornstein-Uhlenbeck process with a drift taking values in the Cameron-Martin space. We study the infinitesimal generator, and a partial integration onC[0,1] will yield conditions on the drift which enable us to use arguments of perturbation theory to prove the existence of an invariant measure which is absolutely continuous with respect to the Wiener measure. 相似文献
11.
Ravi Chari 《Journal of Theoretical Probability》1990,3(1):9-29
We prove the existence and uniquencess of the solution to the martingale problem associated with jump-type Ornstein-Uhlenbeck processes in the Schwartz space of distributions onR
d. An example of a noninteracting infinite-particle system is given, which after rescaling has such a process as a limit. Cases when such a process has an invariant measure are identified. 相似文献
12.
Jérôme Droniou Alain Prignet 《NoDEA : Nonlinear Differential Equations and Applications》2007,14(1-2):181-205
We consider the nonlinear heat equation (with Leray-Lions operators) on an open bounded subset of RN with Dirichlet homogeneous boundary conditions. The initial condition is in L1 and the right hand side is a smooth measure. We extend a previous notion of entropy solutions and prove that they coincide
with the renormalized solutions. 相似文献
13.
In this article, we give necessary and sufficient conditions for the existence of a weak solution of a Kolmogorov equation perturbed by an inverse-square potential. More precisely, using a weighted Hardy's inequality with respect to an invariant measure μ, we show the existence of the semigroup solution of the parabolic problem corresponding to a generalized Ornstein–Uhlenbeck operator perturbed by an inverse-square potential in L 2(? N ,?μ). In the case of the classical Ornstein–Uhlenbeck operator we obtain nonexistence of positive exponentially bounded solutions of the parabolic problem if the coefficient of the inverse-square function is too large. 相似文献
14.
B. R. Mykhal’chuk 《Ukrainian Mathematical Journal》1999,51(3):406-418
We constructively prove the theorem of existence of an interpolation integral chain fraction for a nonlinear functionalF:Q[0,1]→R
1.
Kiev University, Kiev. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 51, No. 3, pp. 364–375, March, 1999. 相似文献
15.
Marius Paicu 《偏微分方程通讯》2013,38(8):1107-1140
ABSTRACT We study the periodic Navier–Stokes equation when the vertical viscosity vanishes, in a critical space (invariant by scaling). We shall prove local-in-time existence of the solution. When the tridimensional part of the initial data is small compared with the bidimesional part and with the horizontal viscosity, we shall show global existence of solutions. 相似文献
16.
Zhaoli Liu 《数学学报(英文版)》2000,16(3):505-514
Abstract
This paper is concerned with the existence of periodic solutions for a nonlinear system of ordinary differential equations.
We obtain a Nagumo-type a priori bound for the periodic solutions and then by using this a priori bound we prove the existence of at least one T-periodic solution under some general conditions
Research supported by the NNSF of China and the RFDP of China. 相似文献
17.
We prove the global existence and uniqueness of admissible weak solutions to an asymptotic equation of a nonlinear hyperbolic
variational wave equation with nonnegative L
2(ℝ) initial data.
The work of Ping Zhang is supported by the Chinese postdoctor’s foundation, and that of Yuxi Zheng is supported in part by
NSF DMS-9703711 and the Alfred P. Sloan Research Fellows award. 相似文献
18.
《随机分析与应用》2013,31(6):1421-1486
Abstract In this article we investigate a class of non-autonomous, semilinear, parabolic systems of stochastic partial differential equations defined on a smooth, bounded domain 𝒪 ? ? n and driven by an infinite-dimensional noise defined from an L 2(𝒪)-valued Wiener process; in the general case the noise can be colored relative to the space variable and white relative to the time variable. We first prove the existence and the uniqueness of a solution under very general hypotheses, and then establish the existence of invariant sets along with the validity of comparison principles under more restrictive conditions; the main ingredients in the proofs of these results consist of a new proposition concerning Wong–Zakaï approximations and of the adaptation of the theory of invariant sets developed for deterministic systems. We also illustrate our results by means of several examples such as certain stochastic systems of Lotka–Volterra and Landau–Ginzburg equations that fall naturally within the scope of our theory. 相似文献
19.
We give a new variational approach toL
p
-potential theory for sub-Markovian semigroups. It is based on
the observation that the Gâteaux-derivative of the corresponding
L
p-energy
functional is a monotone operator. This allows to apply the well established
theory of Browder and Minty on monotone operators to the nonlinear problems
in L
p-potential theory.
In particular, using this approach it is possible to avoid any symmetry assumptions of
the underlying semigroup. We prove existence of corresponding
(r, p)-equilibrium potentials and obtain
a complete characterization in terms of a variational inequality. Moreover we
investigate associated potentials and encounter a natural interpretation of the
so-called nonlinear potential operator in the context of monotone operators. 相似文献
20.
Giuseppe Da Prato Hélène Frankowska 《NoDEA : Nonlinear Differential Equations and Applications》2006,12(4):481-501
In this paper we consider a stochastic flow in Rn which leaves a closed convex set K invariant. By using a recent characterization of the invariance, involving the distance function, we study the corresponding
transition semigroup Pt and its infinitesimal generator N. Due to the invariance property, N is a degenerate elliptic operator. We study existence of an invariant measure ν of Pt and the realization of N in L2 (H, ν). 相似文献