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Heat transfer for Marangoni convection over a vapor-liquid interface due to an imposed temperature gradient

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Journal of University of Science and Technology Beijing 2008年第4期15卷 385-388页

作者： Xiaoyan Sheng Liancun Zheng Xinxin Zhang School of Applied Science University of Science and Technology Beijing Beijing 100083 China School of Mechanical Engineering University of Science and Technology Beijing Beijing 100083 China

A similarity analysis for Marangoni convection induced flow over a vapor-liquid interface due to an imposed temperature gradient was carried out. The analysis assumes that the surface tension varies linearly with temperature but the temperature variation is a power law function of the location. The similarity solutions are presented numerically and the associated transfer characteristics are discussed.

关键词： Marangoni convection vapor-liquid interface heat transfer nonlinear boundary value problem

SINGULAR　PERTURBATIONS　FOR　A　CLASS　OF　boundary　value　problemS　OF　HIGHER　ORDER　nonlinear　DIFFERENTIAL　EQUATIONS

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Applied Mathematics and Mechanics(English Edition) 1996年第12期17卷 1193-1201页

作者：史玉明刘光旭 Department of Mathematics Qufu Normal University Qufu P. R. China Department of Mathematics Nankai University Tianjin P. R. China

In this paper, it has been studied that the singular perturbations for the higherorder nonlinear boundary value problem of the formε2y(n)=f(t, ε, y. '', y(n-2))pj(ε)y(1)(0, ε)-qj(ε)y(j+1)(0. ε)=Aj(ε) (0≤j≤n-3)a1(ε)u(n-2)(0.ε)-a2(ε)y(n-1)(0, ε)=B(ε)b1(ε)y(n-2)(1, ε)+b2(ε)y(n-1),(1. ε)=C(ε)by the method of higher order differential inequalities and boundary layer *** some mild conditions, the existence of the perturbed solution is proved and itsuniformly efficient asymptotic expansions up to its n-th order derivative function aregiven out. Hence, the existing results are extended and improved.

关键词： nonlinear boundary value problem singular perturbation,uniformly efficient asymptotic expansion higher orderdifferential inequalities boundary layer correction

Blow-up *** Finiteness for an Evolution p-Laplace System with nonlinear boundary Conditions

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Communications in Mathematical Research 2009年第4期25卷 309-317页

作者： WU XUE-SONG GAO WEN-JIE School of Mathematics Jilin University Changchun 130012

In this paper, the authors consider the positive solutions of the system of the evolution p-Laplacian equationswith nonlinear boundary conditionsand the initial data （u0, v0）, where Ω is a bounded domain in Rn with smooth boundary δΩ, p 〉 2, h（·,·） and s（·,· ） are positive C1 functions, nondecreasing in each variable. The authors find conditions on the functions f, g, h, s that prove the global existence or finite time blow-up of positive solutions for every （u0, v0）.

关键词： nonlinear boundary value problem evolution p-Laplace system blowup

On energy boundary layer equations in power law non-Newtonian fluids

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On energy boundary layer equations in power law non-Newtonia...