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Limiting Behavior of Random Attractors of Stochastic Supercritical Wave Equations Driven by Multiplicative Noise
This paper deals with the limiting behavior of random attractors of stochastic wave equations with supercritical drift driven by linear...
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Fractal dimension of random invariant sets and regular random attractors for stochastic hydrodynamical equations
The main aim of this work is to provide some general and unified results on the existence, regularity and finite fractal dimension estimates of...
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Multiscale Analysis of Semilinear Damped Stochastic Wave Equations
In this paper we proceed with the multiscale analysis of semilinear damped stochastic wave motions. The analysis is made by combining the well-known...
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Macroscopic Multi-fractality of Gaussian Random Fields and Linear Stochastic Partial Differential Equations with Colored Noise
We consider the linear stochastic heat and wave equations with generalized Gaussian noise that is white in time and spatially correlated. Under the...
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Theory and methods for random differential equations: a survey
In this survey, we present an overview of random differential equations, focusing on strong solutions and methods for estimation of statistics and...
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Central limit theorems for nonlinear stochastic wave equations in dimension three
In this paper, we consider three-dimensional nonlinear stochastic wave equations driven by the Gaussian noise which is white in time and has some...
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Several Continuities of a Pullback Random Attractor for Stochastic Non-Autonomous Zakharov Lattice Equations
We study the dynamics of stochastic Zakharov lattice equations driven by multiplicative white noise and time-dependent forces. We first deduce a...
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Renormalization of stochastic nonlinear heat and wave equations driven by subordinate cylindrical Brownian noises
In this paper, we study the stochastic nonlinear heat equations (SNLH) and stochastic nonlinear wave equations (SNLW) on two-dimensional torus
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Non-linear Young equations in the plane and pathwise regularization by noise for the stochastic wave equation
We study pathwise regularization by noise for equations on the plane in the spirit of the framework outlined by Catellier and Gubinelli (Stoch...
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Global well-posedness of the two-dimensional stochastic viscous nonlinear wave equations
We study well-posedness of viscous nonlinear wave equations (vNLW) on the two-dimensional torus with a stochastic forcing. In particular, we prove...
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Stability of Pullback Random Attractors for Stochastic 3D Navier-Stokes-Voight Equations with Delays
This paper is concerned with the limiting dynamics of stochastic retarded 3D non-autonomous Navier-Stokes-Voight (NSV) equations driven by...
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Random Walks
This chapter deals with the random walkRandom walks problem and its connections with the diffusion processes. Its first part is dedicated to an...
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On the Small-Mass Limit for Stationary Solutions of Stochastic Wave Equations with State Dependent Friction
We investigate the convergence, in the small mass limit, of the stationary solutions of a class of stochastic damped wave equations, where the...
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Solving the backward problem for time-fractional wave equations by the quasi-reversibility regularization method
This paper is devoted to the backward problem of determining the initial value and initial velocity simultaneously in a time-fractional wave...
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A Symmetric Fractional-order Reduction Method for Direct Nonuniform Approximations of Semilinear Diffusion-wave Equations
We introduce a symmetric fractional-order reduction (SFOR) method to construct numerical algorithms on general nonuniform temporal meshes for...
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Random tensors, propagation of randomness, and nonlinear dispersive equations
We introduce the theory of random tensors , which naturally extends the method of random averaging operators in our earlier work (Deng et al. in:...
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Algorithm for Solving the Four-Wave Kinetic Equation in Problems of Wave Turbulence
AbstractWe propose the method for numerical solution of four-wave kinetic equations that arise in the wave turbulence (weak turbulence) theory when...
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Partial Differential Equations I Basic Theory
The first of three volumes on partial differential equations, this one introduces basic examples arising in continuum mechanics, electromagnetism,...
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Weak Convergence Rates for Spatial Spectral Galerkin Approximations of Semilinear Stochastic Wave Equations with Multiplicative Noise
Stochastic wave equations appear in several models for evolutionary processes subject to random forces, such as the motion of a strand of DNA in a...
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Well-posedness for the Cahn-Hilliard-Navier-Stokes Equations with Random Initial Data
We consider the almost sure well-posedness of the Cauchy problem to the Cahn-Hilliard-Navier-Stokes equations with a randomization initial data on a...