Abstract
In this paper the singularly perturbed initial boundary value problems for the nonlocal reaction diffusion system are considered. Using the iteration method and the comparison theorem, the existence and its asymptotic behavior of solution for the problem are studied.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
de Jager, E. M., Jiang Furu, The Theory of Singular Perturbation, Amsterdam: North-Holland Publishing Co., 1996.
Kevorkian, J., Cole, J. D., Multiple Scale and Singular Perturbation Methods, New York: Springer-Verlag, 1996.
O’Malley, R. E. Jr., On the asymptotic solution of the singularly perturbed boundary value problems posed by Bohé, J. Math. Anal. Appl., 2000,242:18–38.
Butuzov, V. F., Nefedov, N. N., Schneider, K. R., Singularly perturbed elliptic problems in the case of exchange of stabilities, J. Differential Equations, 2001,169;373–395.
Kelley, W. G., A singular perturbation problem of Carrier and Pearson, J. Math, Anal. Appl., 2001,255:678–697.
Mizoguchi, N., Yanagida, E., Life span of solutions for a semilinear parabolic problem with small diffusion, J. Math. Anal. Appl., 2001,261,350–368.
Mo Jiaqi, A singularly perturbed nonlinear boundary value problem, J. Math. Anal. Appl., 1993,178(1):289–293.
Mo Jiaqi, A class of singularly perturbed boundary value problems for nonlinear differential systems, Systems Sci. Math. Sci., 1999,12(1):55–58.
Mo Jiaqi, Singular perturbation for a class of nonlinear reaction diffusion systems, Science in China, Ser. A, 1989,32(11):1306–1315.
Mo Jiaqi, The singularly perturbed problem for combustion reaction diffusion, Acta Math. Appl. Sinica, 2001,17(2):255–259.
Mo Jiaqi, Han Xianglin, A class of singularly perturbed generalized solution for the reaction diffusion problems, Systems Sci. Math. Sci., 2002,22(4):447–451.
Mo Jiaqi, Shao, S., The singularly perturbed boundary value problems for higher-order semilinear elliptic equations, Advances in Math., 2001,30(2):141–148.
Mo Jiaqi, Ouyang Cheng, A class of nonlocal boundary value problems of nonlinear elliptic systems in unbounded domains, Acta Math. Sci., 2001,21(1):93–97.
Mo Jiaqi, A class of nonlocal singularly perturbed problems for nonlinear hyperbolic differenttial equations, Acta Math. Appl. Sinica, 2001,17(4):469–474.
Mo Jiaqi, Wang Hui, A class of nonlinear nonlocal singularly perturbed problems for reaction diffusion equations, J. Biomathematics, 2002,17(2):143–148.
Mo Jiaqi, Wang Hui, The shock solution for quasilinear singularly perturbed Robin problem, Progress in Natural Sci., 2002,12:945–947.
Author information
Authors and Affiliations
Additional information
Supported by Important Study Project of the National Natural Science Foundation of China (90211004) and by the “Hundred Talents Project” of Chinese Academy of Sciences.
Rights and permissions
About this article
Cite this article
Jiaqi, M. A class of nonlinear singularly perturbed nonlocal reaction diffusion system. Appl. Math. Chin. Univ. 18, 403–411 (2003). https://doi.org/10.1007/s11766-003-0067-5
Received:
Issue Date:
DOI: https://doi.org/10.1007/s11766-003-0067-5