Results 21 to 30 of about 130 (114)

On a stochastic Burgers equation with Dirichlet boundary conditions

International Journal of Mathematics and Mathematical Sciences, Volume 2003, Issue 43, Page 2735-2746, 2003., 2003
We consider the one‐dimensional Burgers equation perturbed by a white noise term with Dirichlet boundary conditions and a non‐Lipschitz coefficient. We obtain existence of a weak solution proving tightness for a sequence of polygonal approximations for the equation and solving a martingale problem for the weak limit.
Ekaterina T. Kolkovska
wiley   +1 more source

Global boundedness to a 3D chemotaxis-Stokes system with porous medium cell diffusion and general sensitivity

Advances in Nonlinear Analysis, 2022
In this article, we will develop an analytical approach to construct the global bounded weak solutions to the initial-boundary value problem of a three-dimensional chemotaxis-Stokes system with porous medium cell diffusion Δnm\Delta {n}^{m} for m≥6563m ...
Tian Yu, Xiang Zhaoyin
doaj   +1 more source

Existence of weak solutions for a scale similarity model of the motion of large eddies in turbulent flow

Journal of Applied Mathematics, Volume 2003, Issue 9, Page 429-446, 2003., 2003
In turbulent flow, the normal procedure has been seeking means u¯ of the fluid velocity u rather than the velocity itself. In large eddy simulation, we use an averaging operator which allows for the separation of large‐ and small‐length scales in the flow field. The filtered field u¯ denotes the eddies of size O(δ) and larger.
Meryem Kaya
wiley   +1 more source

New Lower Bounds on the Radius of Spatial Analyticity for the Third‐Order Nonlinear Schrödinger Equation

Journal of Applied Mathematics, Volume 2026, Issue 1, 2026.
In this paper, we consider the initial value problem associated with the cubic nonlinear Schrödinger equation with third‐order dispersion ∂tu+iα∂x2u+β∂x3u+iγu2u=0,x∈ℝ,t∈ℝ,ux,0=u0x, where α, β and γ are real constants such that β, γ ≠ 0, u is a complex valued function and the initial data u0 is analytic on ℝ and has a uniform radius of analyticity σ0 in
Tegegne Getachew, Xiasheng Shi
wiley   +1 more source

MHD Equations in a Bounded Domain

Annales Mathematicae Silesianae, 2021
We consider the MHD system in a bounded domain Ω ⊂ ℝN, N = 2; 3, with Dirichlet boundary conditions. Using Dan Henry’s semigroup approach and Giga–Miyakawa estimates we construct global in time, unique solutions to fractional approximations of the MHD ...
Kania Maria B.
doaj   +1 more source

Asymptotic expansion of small analytic solutions to the quadratic nonlinear Schrödinger equations in two‐dimensional spaces

International Journal of Mathematics and Mathematical Sciences, Volume 29, Issue 9, Page 501-516, 2002., 2002
We study asymptotic behavior in time of global small solutions to the quadratic nonlinear Schrödinger equation in two‐dimensional spaces i∂tu + (1/2)Δu = 𝒩(u), (t, x) ∈ ℝ × ℝ2; u(0, x) = φ(x), x ∈ ℝ2, where 𝒩(u)=Σj,k=12(λjk(∂xju)(∂xku)+μjk(∂xju¯)(∂xku¯)), where λjk, μjk ∈ ℂ.
Nakao Hayashi, Pavel I. Naumkin
wiley   +1 more source

Structural Stability of the Moore–Gibson–Thompson Heat Equation in a Semi‐Infinite Cylindrical Domain

Journal of Mathematics, Volume 2026, Issue 1, 2026.
This work analyzes the continuous dependence of solutions to the Moore–Gibson–Thompson (MGT) equation formulated via Green–Naghdi Type III second gradient elasticity theory. The governing system is defined on a semi‐infinite cylindrical domain, subject to homogeneous Dirichlet conditions on the lateral boundary.
Jincheng Shi, Yiwu Lin, Smritijit Sen
wiley   +1 more source

Convex dynamics in Hele‐Shaw cells

International Journal of Mathematics and Mathematical Sciences, Volume 31, Issue 11, Page 639-650, 2002., 2002
We study geometric properties of a contracting bubble driven by a homogeneous source at infinity and surface tension. The properties that are preserved during the time evolution are under consideration. In particular, we study convex dynamics of the bubble and prove that the rate of the area change is controlled by variation of the bubble logarithmic ...
Dmitri Prokhorov, Alexander Vasil′ev
wiley   +1 more source

Spatial Decay Estimates for Elastic Plate System With Type II Heat Conduction

Journal of Mathematics, Volume 2026, Issue 1, 2026.
The classical Saint‐Venant principle has been extensively studied for harmonic and biharmonic models but remains largely unexplored for thermomechanical plates governed by hyperbolic (Type II) heat conduction, a conservative thermal model with unique dynamical features. This paper investigates the spatial decay properties of solutions to such a coupled
Jincheng Shi, Yiwu Lin, Pramita Mishra
wiley   +1 more source

Existence of global solution for a differential system with initial data in Lp

International Journal of Mathematics and Mathematical Sciences, Volume 22, Issue 4, Page 823-834, 1999., 1999
In this paper, we study the system governing flows in the magnetic field within the earth. The system is similar to the magnetohydrodynamic (MHD) equations. By establishing a new priori estimates and following Calderón′s procedure for the Navier Stokes equations [1], we obtained, for initial data in space Lp, the global in time existence and uniqueness
Peter Bates, Fengxin Chen, Ping Wang
wiley   +1 more source