A Class of Nonlinear Nonlocal Singularly Perturbed Problems for Reaction Diffusion Equations With Boundary Perturbation

MO Jia-qi; WANG Hui; LIN Wan-tao

Article Contents

Article Navigation > Applied Mathematics and Mechanics > 2005 > 26(12): 1507-1511

MO Jia-qi, WANG Hui, LIN Wan-tao. A Class of Nonlinear Nonlocal Singularly Perturbed Problems for Reaction Diffusion Equations With Boundary Perturbation[J]. Applied Mathematics and Mechanics, 2005, 26(12): 1507-1511.

Citation:

PDF( 2229 KB)

A Class of Nonlinear Nonlocal Singularly Perturbed Problems for Reaction Diffusion Equations With Boundary Perturbation

1.
Department of Mathematics, Anhui Normal University, Wuhu, Anhui 241000, P. R. China;

Received Date: 2003-09-15
Rev Recd Date: 2005-04-03
Publish Date: 2005-12-15

Abstract

Abstract

A class of nonlinear nonlocal for singularly perturbed Robin initial boundary value problems for reaction diffusion equations with boundary perturbation is considered.Under suitable conditions,first,the outer solution of the original problem was obtained.Secondly,using the stretched variable,the composing expansion method and the expanding theory of power series the initial layer was constructed.Finally,using the theory of differential inequalities the asymptotic behavior of solution for the initial boundary value problems was studied,and educing some relational inequalities the existence and uniqueness of solution for the original problem and the uniformly valid asymptotic estimation were discussed.
- nonlinear,
- reaction diffusion,
- singular perturbation

FullText(HTML)

References(9)

References

[1]	de Jager E M,JIANG Fu-ru.The Theory of Singular Perturbation[M].Amsterdam:North-Holland Publishing Company,1996.
[2]	Hamouda M.Interior layer for second-order singular equations[J].Applicable Analysis,2002,81(2):837—866. doi: 10.1080/0003681021000004465
[3]	Bell D C,Deng B.Singular perturbation of N-front traveling waves in the Fitzhugh-Nagumo equations[J].Nonlinear Analysis Real World Applications,2003,3(4):515—541.
[4]	do Nascimento A S.Stable transition layers in a semilinear diffusion equation with spatial inhomogeneties in N-dimensional domains[J].Journal of Differential Equations,2003,190(1):16—38. doi: 10.1016/S0022-0396(02)00147-X
[5]	MO Jia-qi.Singular perturbation for a class of nonlinear reaction diffusion systems[J].Science in China,Ser A,1989,32(11):1306—1315.
[6]	MO Jia-qi,Shao S.The singularly perturbed boundary value problems for higher-order semilinear elliptic equations[J].Advances in Mathematics,2001,30(2):141—148.
[7]	MO Jia-qi,OUYANG Cheng.A class of nonlocal boundary value problems of nonlinear elliptic systems in unbounded domains[J].Acta Mathematica Scientia,2001,21(1):93—97.
[8]	MO Jia-qi.A class of nonlocal singularly perturbed problems for nonlinear hyperbolic differential equation[J].Acta Mathematicae Applicatae Sinica,2001,17(4):469—474. doi: 10.1007/BF02669699
[9]	MO Jia-qi,ZHU Jiang,WANG Hui.Asymptotic behavior of the shock solution for a class of nonlinear equations[J].Progress in Natural Science,2003,13(9):768—770. doi: 10.1080/10020070312331344400