具有脉冲源项的二阶半线性奇摄动边值问题
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摘要
研究一类具有典型脉冲源项的二阶奇摄动边值问题,用合成展开法构造出其渐近解,然后用微分不等式定理证明了原问题解的存在性和形式渐近解的一致有效性,最后给出例子.
A class of second-order singularly perturbed boundary value problems with a pulse source term is studied. Its asymptotic solution is constructed by the composite expansion method. The existence of solution to the original problem and the uniformly validity of the formal asymptotic solution are proved by using the theorem of differential inequalities. Finally, an example is presented as an illustration.
A class of second-order singularly perturbed boundary value problems with a pulse source term is studied. Its asymptotic solution is constructed by the composite expansion method. The existence of solution to the original problem and the uniformly validity of the formal asymptotic solution are proved by using the theorem of differential inequalities. Finally, an example is presented as an illustration.
引文
[1]周明儒,林武忠,倪明康,等.奇异摄动导论[M].北京:科学出版社,2014.
[2]刘树德,鲁世平,姚静荪,等.奇异摄动边界层和内层理论[M].北京:科学出版社,2012.
[3]周明儒,杜增吉,王广瓦.奇异摄动中的微分不等式理论[M].北京:科学出版社,2012.
[4]倪明康,林武忠.奇异摄动问题中的空间对照结构理论[M].北京:科学出版社,2014.
[5]LIN?T.Finite difference schemes for convection-diffusion problems with a concentrated source and a discontinuous convection field[J].Computational Methods in Applied Mathematics,2002,2(1):41-49.
[6]GRACIA J L,O’RIORDAN E.A singularly perturbed convection-diffusion problem with a moving pulse[J].Journal of Computational and Applied Mathematics,2017,321:371-388.
[7]BRAYANOV I A.Numerical solution of a two-dimensional singularly perturbed reaction-diffusion problem with discontinuous coefficients[J].Applied Mathematics and Computation,2006,182(1):631-643.
[8]XIE F.An interface problem with singular perturbation on a subinterval[J].Boundary Value Problems,2014,2014:1-11.
[9]LIN H,XIE F.Singularly perturbed second order semilinear boundary value problems with interface conditions[J].Boundary Value Problems,2015,2015:1-16.
[10]CHANG K W,HOWES F A.Nonlinear Singular Perturbation Phenomena:Theory and Application[M].New York:Springer-Verlag,1984.
[2]刘树德,鲁世平,姚静荪,等.奇异摄动边界层和内层理论[M].北京:科学出版社,2012.
[3]周明儒,杜增吉,王广瓦.奇异摄动中的微分不等式理论[M].北京:科学出版社,2012.
[4]倪明康,林武忠.奇异摄动问题中的空间对照结构理论[M].北京:科学出版社,2014.
[5]LIN?T.Finite difference schemes for convection-diffusion problems with a concentrated source and a discontinuous convection field[J].Computational Methods in Applied Mathematics,2002,2(1):41-49.
[6]GRACIA J L,O’RIORDAN E.A singularly perturbed convection-diffusion problem with a moving pulse[J].Journal of Computational and Applied Mathematics,2017,321:371-388.
[7]BRAYANOV I A.Numerical solution of a two-dimensional singularly perturbed reaction-diffusion problem with discontinuous coefficients[J].Applied Mathematics and Computation,2006,182(1):631-643.
[8]XIE F.An interface problem with singular perturbation on a subinterval[J].Boundary Value Problems,2014,2014:1-11.
[9]LIN H,XIE F.Singularly perturbed second order semilinear boundary value problems with interface conditions[J].Boundary Value Problems,2015,2015:1-16.
[10]CHANG K W,HOWES F A.Nonlinear Singular Perturbation Phenomena:Theory and Application[M].New York:Springer-Verlag,1984.