Zobrazeno 1 - 10
of 223
pro vyhledávání: '"35R60, 60H15"'
In these lecture notes, we review recent progress in the study of the stochastic heat equation and its discrete analogue, the directed polymer model, in spatial dimension 2. It was discovered that a phase transition emerges on an intermediate disorde
Externí odkaz:
http://arxiv.org/abs/2412.10311
Autor:
Chaudhary, Abhishek
We propose an {\em implementable} numerical scheme for the discretization of linear-quadratic optimal control problems involving SDEs in higher dimensions with {\em control constraint}. For time discretization, we employ the implicit Euler scheme, de
Externí odkaz:
http://arxiv.org/abs/2412.08553
In this paper, we establish the global $L^{p}$ mild solution of inhomogeneous incompressible Navier-Stokes equations in the torus $\mathbb{T}^{N}$ with $N
Externí odkaz:
http://arxiv.org/abs/2409.20418
Publikováno v:
Journal of Dynamics and Differential Equations, Volume 35, 523 - 542, 2023
This article studies the Stochastic Degasperis-Procesi (SDP) equation on $\mathbb{R}$ with an additive noise. Applying the kinetic theory, and considering the initial conditions in $L^2(\mathbb{R})\cap L^{2+\delta}(\mathbb{R})$, for arbitrary small $
Externí odkaz:
http://arxiv.org/abs/2409.00548
Autor:
Ghafari, Joe
We prove local well-posedness of the Cahn-Hilliard equation with additive noise. Our method relies on paracontrolled calculus and the Da Prato-Debussche trick.
Externí odkaz:
http://arxiv.org/abs/2407.20293
Autor:
Li, Binjie, Zhou, Qin
This paper analyzes a full discretization of a three-dimensional stochastic Allen-Cahn equation with multiplicative noise. The discretization combines the Euler scheme for temporal approximation and the finite element method for spatial approximation
Externí odkaz:
http://arxiv.org/abs/2405.03016
We study a parametrically forced nonlinear Schr\"odinger (PFNLS) equation, driven by multiplicative translation-invariant noise. We show that a solitary wave in the stochastic equation is orbitally stable on a timescale which is exponential in the in
Externí odkaz:
http://arxiv.org/abs/2403.04625
We study global-in-time dynamics of the stochastic nonlinear beam equations (SNLB) with an additive space-time white noise, posed on the four-dimensional torus. The roughness of the noise leads us to introducing a time-dependent renormalization, afte
Externí odkaz:
http://arxiv.org/abs/2312.13901
Autor:
Fritz, Marvin, Scarpa, Luca
In this work, we present and analyze a system of PDEs, which models tumor growth by considering chemotaxis, active transport, and random effects. The stochasticity of the system is modelled by random initial data and Wiener noises that appear in the
Externí odkaz:
http://arxiv.org/abs/2312.06288
Autor:
Li, Binjie, Zhou, Qin
This study investigates the boundedness of the \( H^\infty \)-calculus for the negative discrete Laplace operator, subject to homogeneous Dirichlet boundary conditions. The negative discrete Laplace operator is implemented using the finite element me
Externí odkaz:
http://arxiv.org/abs/2311.04615