Results 61 to 70 of about 11,370,086 (322)

On classification of global dynamics for energy‐critical equivariant harmonic map heat flows and radial nonlinear heat equation

Communications on Pure and Applied Mathematics, EarlyView.
Abstract We consider the global dynamics of finite energy solutions to energy‐critical equivariant harmonic map heat flow (HMHF) and radial nonlinear heat equation (NLH). It is known that any finite energy equivariant solutions to (HMHF) decompose into finitely many harmonic maps (bubbles) separated by scales and a body map, as approaching to the ...
Kihyun Kim, Frank Merle
wiley   +1 more source

Existence and uniqueness theorem of associated solutions of the stochastic differential system with measures

Журнал Белорусского государственного университета: Математика, информатика, 2018
The Cauchy problem for stochastic differential system with measures is considered in the paper. Finite-difference with averaging system of stochastic differential equations with correspondence to Cauchy problem is investigated.
Artsiom Y. Rusetski
doaj  

The Cauchy problem for singularly perturbed higher-order integro-differential equations

Вестник КазНУ. Серия математика, механика, информатика, 2019
The article is devoted to research the Cauchy problem for singularly perturbed higher-order linear integro-differential equation with a small parameter at the highest derivatives, provided that the roots of additional characteristic equation have ...
A. E. Mirzakulova, M. K. Dauylbaev, M. U. Akhmet, A. K. Dzhetpisbaeva   +3 more
doaj   +1 more source

Boundary conditions and universal finite‐size scaling for the hierarchical |φ|4$|\varphi |^4$ model in dimensions 4 and higher

Communications on Pure and Applied Mathematics, EarlyView.
Abstract We analyse and clarify the finite‐size scaling of the weakly‐coupled hierarchical n$n$‐component |φ|4$|\varphi |^4$ model for all integers n≥1$n \ge 1$ in all dimensions d≥4$d\ge 4$, for both free and periodic boundary conditions. For d>4$d>4$, we prove that for a volume of size Rd$R^{d}$ with periodic boundary conditions the infinite‐volume ...
Emmanuel Michta, Jiwoon Park, Gordon Slade   +2 more
wiley   +1 more source

Cauchy problem for the hyperbolic system with mixed derivative

Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki, 2012
Cauchy problem for the hyperbolic system with mixed derivative is considered. The given system is transformed to the triangular or diagonal form for the further equations separation.
E. A. Kozlova
doaj   +1 more source

Quasi‐invariance of Gaussian measures for the 3d$3d$ energy critical nonlinear Schrödinger equation

Communications on Pure and Applied Mathematics, EarlyView.
Abstract We consider the 3d$3d$ energy critical nonlinear Schrödinger equation with data distributed according to the Gaussian measure with covariance operator (1−Δ)−s$(1-\Delta)^{-s}$, where Δ$\Delta$ is the Laplace operator and s$s$ is sufficiently large. We prove that the flow sends full measure sets to full measure sets. We also discuss some simple
Chenmin Sun, Nikolay Tzvetkov
wiley   +1 more source

On the approximate solution of the Cauchy problem for the Helmholtz equation on the plane [PDF]

Computational Algorithms and Numerical Dimensions
In this paper, approximate solutions of the Cauchy problem for the Helmholtz equation on a two-dimensional bounded region are found. The problem under consideration belongs to the problems of mathematical physics, in which there is no continuous ...
Davron Juraev, Nazira Mammadzada, Praveen Agarwal, Shilpi Jain   +3 more
doaj   +1 more source

A review of multiscale numerical modeling of rock mechanics and rock engineering

Deep Underground Science and Engineering, EarlyView.
Multiscale numerical methods of rock mechanics and rock engineering are reviewed, and the review results show that more attention should be paid to the development of an advanced constitutive model in addition to numerical techniques themselves. Abstract Rock is geometrically and mechanically multiscale in nature, and the traditional phenomenological ...
Xindong Wei, Zhe Li, Gaofeng Zhao
wiley   +1 more source

Damage modeling of CO2 injection well interfaces under coupled thermal, hydraulic and mechanical behavior

Deep Underground Science and Engineering, EarlyView.
This paper presents an investigation of CO2 injection well damage evolution considering different injection temperatures and the presence of a pre‐existing defect. The main outcome is that the accurate prediction of well leakage risk requires characteristics such as initial defects to be understood and represented in any modeling efforts. Abstract This
Lee J. Hosking, Xiangming Zhou
wiley   +1 more source

Asymptotics for fractional reaction diffusion equations in periodic media

AIMS Mathematics
In this paper, the Cauchy problem for a class of reaction diffusion equations are considered with nonlocal interactions in periodic media. First, we demonstrate the existence and uniqueness of solutions that are both positive and bounded for the ...
Yu Wei, Yahan Wang, Huiqin Lu
doaj   +1 more source