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Long time behavior for damped generalized coupled nonlinear wave equations. Ⅱ.Unbounded domain

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Communications in Nonlinear Science and Numerical Simulation 2001年第2期6卷 107-110页

作者： Shaomei FANG and Boling GUO Department of Mathematics, Shaoguan University, Shaoguan 512005, China Graduate School, China Academy of Engineering Physics, Beijing 100088, China Center for Nonlinear Studies, Institute of Applied Physics and Computational Department of Mathematics Shaoguan University Shaoguan 512005 China Graduate School China Academy of Engineering Physics Beijing 100088 China Center for Nonlinear Studies Institute of Applied Physics and Computational mathematics Beijing 100088 China

In this paper, by using a priori estimates in the weighted space, the existence of the global attractor for the damped generalized coupled nonlinear wave equations in an unbounded domain is obtained.

关键词： unbounded domain weighted space attractor

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ATTRACTORS FOR THE GINZBURG-LANDAU-BBM EQUATIONS IN AN UNBOUNDED DOMAIN

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Acta Mathematica Scientia 2000年第1期20卷 122-130页

作者：郭柏灵蒋慕蓉 Inst Appl Phys & Computat Math Beijing 100088 Peoples R China Yunnan Univ Dept Math Kunming 650091 Peoples R China Chinese Acad Engn Phys Grad Sch Beijing 100088 Peoples R China

By the interpolating inequality and a priori estimates in the weighted space,the existence of the global solutions for the Ginzburg-Landau equation coupled with the BBM equation in an unbounded domain is considered, a... 详细信息

关键词： Unbounded domain weighted space attractor Ginzburg-Landau-BBM equations

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ATTRACTORS FOR GENERALIZED GINZBURG-LANDAU-BBM EQUATIONS IN AN UNBOUNDED DOMAIN

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Acta Mathematicae Applicatae Sinica 2001年第3期17卷 317-325页

作者：蒋慕蓉郭柏灵 Department of Mathematics Yunnan University Kunming China R & D Center for Parallel Software Institute of Software Chinese Academy of Sciences Beijing China Institute of Applied Physics and Computational Mathematics Beijing China

By the interpolation inequality and a priori estimates in the weighted space, the existence of global solutions for generalized Ginzburg-Landau equation coupled with BBM equation in an unbounded domain is considered, ... 详细信息

关键词： unbounded domain weighted space attractor generalized Ginzburg-Landau-BBM equations

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Applications of Non-Classical Equations and Their Approaches to the Solution of Some of Classes Equations Arise in the Kelvin-Helmholtz Mechanism and Instability

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Open Journal of Applied Sciences 2022年第11期12卷 1873-1891页

作者： Mahammad A. Nurmammadov Shamakhi Astropysical Observatory Named after Nasreddin Tusi of Ministry of Sciences and Education of the Republic Azerbaijan Shamakhi Azerbaijan

In the presented work, we consider applications of non-classical equations and their approaches to the solution of some classes of equations that arise in the Kelvin-Helmholtz Mechanism (KHM) and instability. In all areas where the Kelvin-Helmholtz instability (KHI) problem is investigated with the corresponding data unchanged, the solution can be taken directly in a specific form (for example, to determine the horizontal structure of a perturbation in a barotropic rotational flow, which is a boundary condition taken, as well as other types of Kelvin-Helmholtz instability problems). In another example, the shear flow along the magnetic field in the Z direction, which is the width of the contact layer between fast and slow flows, has a velocity gradient along the X axis with wind shear. The most difficult problems arise when the above unmentioned equation has singularities simultaneously at points and in this case, our results also remain valid. In the case of linear wave analysis of Kelvin-Helmholtz instability (KHI) at a tangential discontinuity (TD) of ideal magneto-hydro-dynamic (MHD) plasma, it can be attributed to the presented class, and in this case, as far as we know, solutions for eigen modes of instability KH in MHD plasma that satisfy suitable homogeneous boundary conditions. Based on the above mentioned area of application for degenerating ordinary differential equations in this work, the method of functional analysis in order to prove the generalized solution is used. The investigated equation covers a class of a number of difficult-to-solve problems, namely, generalized solutions are found for classes of problems that have analytical and mathematical descriptions. With the aid of lemmas and theorems, the existence and uniqueness of generalized solutions in the weight space are proved, and then general and particular exact solutions are found for the considered problems that are expressed analytically explicitly. Obtained our results may be used for all

关键词： Kelvin-Helmholtz Mechanism and Instability Ordinary Differential Equations weighted space Degenerating Planetary Jupiter Non-Classical Approaches