scholarly journals Regular attractors of asymptotically autonomous stochastic 3D Brinkman-Forchheimer equations with delays

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Qiangheng Zhang ◽  
Yangrong Li
Keyword(s):  
Lipschitz Condition ◽  
Stochastic Equation ◽  
Distributed Delay ◽  
Time Parameter ◽  
Random Attractor ◽  
Regular Space ◽  
Variable Delay ◽  
Lipschitz Continuous ◽  
Initial Space

<p style='text-indent:20px;'>We study asymptotically autonomous dynamics for non-autonom-ous stochastic 3D Brinkman-Forchheimer equations with general delays (containing variable delay and distributed delay). We first prove the existence of a pullback random attractor not only in the initial space but also in the regular space. We then prove that, under the topology of the regular space, the time-fibre of the pullback random attractor semi-converges to the random attractor of the autonomous stochastic equation as the time-parameter goes to minus infinity. The general delay force is assumed to be pointwise Lipschitz continuous only, which relaxes the uniform Lipschitz condition in the literature and includes more examples.</p>

Global random attractor of stochastic hydrodynamical equation for the Heisenberg paramagnet with multiplicative noise on ℝd

2015 ◽  
Vol 16 (01) ◽  
pp. 1650007 ◽  
Author(s):  
Yanfeng Guo ◽  
Chunxiao Guo ◽  
Yongqian Han
Keyword(s):  
Dynamical System ◽  
Multiplicative Noise ◽  
Stochastic Equation ◽  
Random Coefficients ◽  
Random Attractor ◽  
Random Dynamical System ◽  
Hydrodynamical Equation ◽  
Priori Estimates ◽  
Heisenberg Paramagnet ◽  
Truncation Function

The stochastic hydrodynamical equation for the Heisenberg paramagnet with multiplicative noise defined on the entire [Formula: see text] is mainly investigated. The global random attractor for the random dynamical system associated with the equation is obtained. The method is to transform the stochastic equation into the corresponding partial differential equations with random coefficients by Ornstein–Uhlenbeck process. The uniform priori estimates for far-field values of solutions have been studied via a truncation function, and then the asymptotic compactness of the random dynamical system is established.

scholarly journals Random Attractors for Stochastic Retarded 2D-Navier-Stokes Equations with Additive Noise

2018 ◽  
Vol 2018 ◽  
pp. 1-14
Author(s):  
Xiaoyao Jia ◽  
Xiaoquan Ding
Keyword(s):  
Additive Noise ◽  
Stochastic Equation ◽  
Stokes Equations ◽  
Upper Semicontinuity ◽  
Random Attractor ◽  
Navier Stokes ◽  
Pullback Attractor ◽  
Navier Stokes Equation ◽  
Navier Stokes Equations ◽  
Random Attractors

In this paper, the existence and the upper semicontinuity of a pullback attractor for stochastic retarded 2D-Navier-Stokes equation on a bounded domain are obtained. We first transform the stochastic equation into a random equation and then obtain the existence of a random attractor for random equation. Then conjugation relation between two random dynamical systems implies the existence of a random attractor for the stochastic equation. At last, we get the upper semicontinuity of random attractor.

scholarly journals Moment Bound of Solution to a Class of Conformable Time-Fractional Stochastic Equation

2019 ◽  
Vol 3 (2) ◽  
pp. 18
Author(s):  
McSylvester Omaba ◽  
Eze Nwaeze
Keyword(s):  
Fractional Derivative ◽  
Existence And Uniqueness ◽  
Random Function ◽  
Stochastic Equation ◽  
Initial Condition ◽  
Lipschitz Continuous ◽  
Fractional Heat Equation ◽  
Upper Bound Estimate ◽  
Time Fractional Derivative ◽  
Uniqueness Of A Solution

We study a class of conformable time-fractional stochastic equation T α , t a u ( x , t ) = σ ( u ( x , t ) ) W ˙ t , x ∈ R , t ∈ [ a , T ] , T < ∞ , 0 < α < 1 . The initial condition u ( x , 0 ) = u 0 ( x ) , x ∈ R is a non-random function assumed to be non-negative and bounded, T α , t a is a conformable time-fractional derivative, σ : R → R is Lipschitz continuous and W ˙ t a generalized derivative of Wiener process. Some precise condition for the existence and uniqueness of a solution of the class of equation is given and we also give an upper bound estimate on the growth moment of the solution. Unlike the growth moment of stochastic fractional heat equation with Riemann–Liouville or Caputo–Dzhrbashyan fractional derivative which grows in time like t c 1 exp ( c 2 t ) , c 1 , c 2 > 0 ; our result also shows that the energy of the solution (the second moment) grows exponentially in time for t ∈ [ a , T ] , T < ∞ but with at most c 1 exp ( c 2 ( t − a ) 2 α − 1 ) for some constants c 1 , and c 2 .

scholarly journals On the One-Leg Methods for Solving Nonlinear Neutral Differential Equations with Variable Delay

2012 ◽  
Vol 2012 ◽  
pp. 1-27 ◽  
Author(s):  
Wansheng Wang ◽  
Shoufu Li
Keyword(s):  
Differential Equations ◽  
Lipschitz Condition ◽  
Error Bounds ◽  
Natural Question ◽  
Variable Delay ◽  
Neutral Differential Equations ◽  
The One ◽  
Error Behavior ◽  
Lipschitz Conditions

Based onA-stable one-leg methods and linear interpolations, we introduce four algorithms for solving neutral differential equations with variable delay. A natural question is which algorithm is better. To answer this question, we analyse the error behavior of the four algorithms and obtain their error bounds under a one-sided Lipschitz condition and some classical Lipschitz conditions. After extensively numerically experimenting, we give a positive conclusion.

scholarly journals Random Attractors for Stochastic Retarded Reaction-Diffusion Equations on Unbounded Domains

2013 ◽  
Vol 2013 ◽  
pp. 1-16 ◽  
Author(s):  
Xiaoquan Ding ◽  
Jifa Jiang
Keyword(s):  
Diffusion Equation ◽  
Stochastic Equation ◽  
Dimensional Space ◽  
Reaction Diffusion ◽  
Random Attractor ◽  
Reaction Diffusion Equations ◽  
Reaction Diffusion Equation ◽  
Random Dynamical System ◽  
Large Space ◽  
Uniform Estimates

This paper is devoted to a stochastic retarded reaction-diffusion equation on alld-dimensional space with additive white noise. We first show that the stochastic retarded reaction-diffusion equation generates a random dynamical system by transforming this stochastic equation into a random one through a tempered stationary random homeomorphism. Then, we establish the existence of a random attractor for the random equation. And the existence of a random attractor for the stochastic equation follows from the conjugation relation between two random dynamical systems. The pullback asymptotic compactness is proved by uniform estimates on solutions for large space and time variables. These estimates are obtained by a cut-off technique.

Control by Pyragas method with variable delay: from simple models to experiments

2014 ◽  
Vol 1 ◽  
pp. 679-682
Author(s):  
Aleksandar Gjurchinovski ◽  
Thomas Jüngling ◽  
Viktor Urumov
Keyword(s):  
Variable Delay ◽  
Simple Models

A Feed-Forward Time Amplifier Using a Phase Detector and Variable Delay Lines

2013 ◽  
Vol E96.C (6) ◽  
pp. 920-922 ◽  
Author(s):  
Kiichi NIITSU ◽  
Naohiro HARIGAI ◽  
Takahiro J. YAMAGUCHI ◽  
Haruo KOBAYASHI
Keyword(s):  
Phase Detector ◽  
Variable Delay ◽  
Delay Lines ◽  
Feed Forward ◽  
Time Amplifier

Light front field theory: An advanced Primer

2007 ◽  
Vol 57 (3) ◽  
Author(s):  
L'ubomír Martinovič
Keyword(s):  
Field Theory ◽  
Detailed Comparison ◽  
Light Front ◽  
Two Dimensional ◽  
Schwinger Model ◽  
Initial Space ◽  
Model Hamiltonian ◽  
Spatial Volume ◽  
Hamiltonian Perturbation Theory ◽  
Light Front Quantization

Light front field theory: An advanced PrimerWe present an elementary introduction to quantum field theory formulated in terms of Dirac's light front variables. In addition to general principles and methods, a few more specific topics and approaches based on the author's work will be discussed. Most of the discussion deals with massive two-dimensional models formulated in a finite spatial volume starting with a detailed comparison between quantization of massive free fields in the usual field theory and the light front (LF) quantization. We discuss basic properties such as relativistic invariance and causality. After the LF treatment of the soluble Federbush model, a LF approach to spontaneous symmetry breaking is explained and a simple gauge theory - the massive Schwinger model in various gauges is studied. A LF version of bosonization and the massive Thirring model are also discussed. A special chapter is devoted to the method of discretized light cone quantization and its application to calculations of the properties of quantum solitons. The problem of LF zero modes is illustrated with the example of the two-dimensional Yukawa model. Hamiltonian perturbation theory in the LF formulation is derived and applied to a few simple processes to demonstrate its advantages. As a byproduct, it is shown that the LF theory cannot be obtained as a "light-like" limit of the usual field theory quantized on an initial space-like surface. A simple LF formulation of the Higgs mechanism is then given. Since our intention was to provide a treatment of the light front quantization accessible to postgradual students, an effort was made to discuss most of the topics pedagogically and a number of technical details and derivations are contained in the appendices.

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