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SINGULARLY_PERTURBED: 作品数：204被引量：398H指数：11; 导出分析报告; 相关作者：莫嘉琪陈松林王庚鲁世平袁永军更多>>; 相关机构：安徽师范大学华东冶金学院安徽机电职业技术学院华东师范大学更多>>; 相关期刊：更多>>; 相关基金：国家自然科学基金国家重点基础研究发展计划上海市自然科学基金福建省自然科学基金更多>>

Chien-physics-informed neural networks for solving singularly perturbed boundary-layer problems: 《Applied Mathematics and Mechanics(English Edition)》2024年第9期1467-1480,共14页Long WANG Lei ZHANG Guowei HE; Project supported by the National Natural Science Foundation of China Basic Science Center Program for“Multiscale Problems in Nonlinear Mechanics”(No.11988102);the National Natural Science Foundation of China(No.12202451)。; A physics-informed neural network(PINN)is a powerful tool for solving differential equations in solid and fluid mechanics.However,it suffers from singularly perturbed boundary-layer problems in which there exist sharp...; 关键词：physics-informed neural network(PINN) singular perturbation boundarylayer problem composite asymptotic expansion

Contrast structure for singular singularly perturbed boundary value problem被引量：1: 《Applied Mathematics and Mechanics(English Edition)》2014年第5期655-666,共12页王爱峰倪明康; Project supported by the National Natural Science Foundation of China(No.11071075);the Natural Science Foundation of Shanghai(No.10ZR1409200); The step-type contrast structure for a singular singularly perturbed problem is shown. By use of the method of boundary function, the formal asymptotic expansion is constructed. At the same time, based on sewing orbit...; 关键词：contrast structure singular singularly perturbation asymptotic expansion boundary function

Step-like contrast structure for class of nonlinear singularly perturbed optimal control problem: 《Applied Mathematics and Mechanics(English Edition)》2013年第7期875-888,共14页武利猛倪明康陆海波; supported by the National Natural Science Foundation of China (Nos. 11071075 and 11171113);the E-Institute of Shanghai Municipal Education Commission (No. E03004);the Knowledge Innovation Program of the Chinese Academy of Sciences (Nos. 30921064 and 90820307); The step-like contrast structure for a class of nonlinear singularly perturbed optimal control problems is considered. The existence of the step-like contrast structure for the singularly perturbed optimal control pro...; 关键词：optimal control contrast structure singular perturbation

Singularly perturbed reaction diffusion equations with time delay被引量：1: 《Applied Mathematics and Mechanics(English Edition)》2010年第6期769-774,共6页莫嘉琪温朝晖; Project supported by the National Natural Science Foundation of China (No. 40876010);the Major Projects of Knowledge Innovation Program of Chinese Academy of Sciences (No. KZCX2-YW-Q03-08);the Research and Development Special Fund for Public Welfare Industry (No. GYHY200806010);the Special Fund of the State Key Laboratory of Numerical Modeling for Atmospheric Sciences and Geophysical Fluid Dynamics, the Foundation of Shanghai Municipal Education Commission(No. E03004);the Natural Science Foundation of Zhejiang Province (No. Y6090164); A class of initial boundary value problems of differential-difference equations for reaction diffusion with a small time delay is considered. Under suitable conditions and by using the stretched variable method, a for...; 关键词：NONLINEAR reaction diffusion singular perturbation time delay

Singularly perturbed solution to semilinear reaction diffusion equations with two parameters: 《Applied Mathematics and Mechanics(English Edition)》2009年第5期653-658,共6页莫嘉琪刘树德; supported by the National Natural Science Foundation of China (Nos.40676016,40876010);the Key Innovation Project of the Chinese Academy of Sciences (No.KZCX2-YW-Q03-08);the E-Institute of Shanghai Municipal Education Commission (No. E03004); A class of singularly perturbed initial boundary value problems for semilinear reaction diffusion equations with two parameters is considered, Under suitable conditions and using the theory of differential inequalitie...; 关键词：nonlinear two parameters singular perturbation reaction diffusion initial layer boundary layer

Singularly perturbed solution for weakly nonlinear equations with two parameters被引量：3: 《Applied Mathematics and Mechanics(English Edition)》2007年第10期1343-1348,共6页陈丽华莫嘉琪; Project supported by the National Natural Science Foundation of China(Nos.40676016 and 10471039);the National Key Project for Basic Research(Nos.2003CB415101-03 and 2004CB418304);the Key Project of the Chinese Academy of Sciences(No.KZCX3-SW-221);in part by E-Insitutes of Shanghai Municipal Education Commission(No.N.E03004);the Natural Science Foundation of Zhejiang Province of China(No.Y606368).; A class of singularly perturbed boundary value problems of weakly non linear equation for fourth order on the interval [a, b] with two parameters is considered. Under suitable conditions, firstly, the reduced solution...; 关键词：NONLINEAR two parameters singular perturbation

STRUCTURE OF NONNEGATIVE NONTRIVIAL AND POSITIVE SOLUTIONS OF SINGULARLY PERTURBED p-LAPLACE EQUATIONS被引量：1: 《Applied Mathematics and Mechanics(English Edition)》2004年第8期929-936,共8页张正策李开泰 LINZong-chi; theNationalKeyBasicResearchDevelopmentProjectProgramofChina(1 9990 3 2 80 1 ) ;theNationalNaturalScienceFoundationofChina (1 0 3 71 0 95); Structure of nonnegative nontrivial and positive solutions was precisely studied for some singularly perturbed p-Laplace equations. By virtue of sub- and supersolution method, it is shown that there are many nonnegati...; 关键词：p-Laplace equation nonnegative nontrivial solution positive solution spike-layer solution sub- and supersolution

SINGULARLY PERTURBED NONLINEAR BOUNDARY VALUE PROBLEM FOR A KIND OF VOLTERRA TYPE FUNCTIONAL DIFFERENTIAL EQUATION: 《Applied Mathematics and Mechanics(English Edition)》2003年第12期1441-1449,共9页鲁世平; theNaturalScienceFoundationofEducationDepartmentofAnhuiProvinceofChina (2 0 0 2kj1 3 3 ); By employing the theory of differential inequality and some analysis methods, a nonlinear boundary value problem subject to a general kind of second_order Volterra functional differential equation was considered first...; 关键词：singular perturbation functional differential equation boundary value problem uniformly valid asymptotic expansion

SINGULARLY PERTURBED BOUNDARY VALUE PROBLEMS FOR SEMI-LINEAR RETARDED DIFFERENTIAL EQUATIONS WITH NONLINEAR BOUNDARY CONDITIONS: 《Applied Mathematics and Mechanics(English Edition)》2003年第12期1450-1455,共6页任景莉葛渭高; theNationalNaturalScienceFoundationofChina (1 9871 0 0 5); A boundary value problems for functional differenatial equations, with nonlinear boundary condition, is studied by the theorem of differential inequality. Using new method to construct the upper solution and lower sol...; 关键词：singular perturbation functional differential equation boundary value problem uniformly valid asymptotic expansion

THIRD-ORDER NONLINEAR SINGULARLY PERTURBED BOUNDARY VALUE PROBLEM被引量：1: 《Applied Mathematics and Mechanics(English Edition)》2002年第6期670-677,共8页WANG Guo-can(王国灿) JIN Li(金丽); Third order singulary perturbed boundary value problem by means of differential inequality theories is studied. Based on the given results of second order nonlinear boundary value problem, the upper and lower solution...; 关键词：third order boundary value problem upper and lower solutions Volterra type integral operator existence and asymptotic estimates

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