Abstract
The singularly perturbed initial boundary value problems for the reaction diffusion system are raised. Firstly, under suitable conditions, using a iteration technique, the differential inequalities theorem is constructed and introducing two auxiliary functions the existence and uniqueness theorem of solution for the basic reaction diffusion system is proved. Using the singularly perturbed method the formal asymptotic expressions of the solution are constructed with power series theory. By using the comparison theorem the existence and its asymptotic behavior of solution for the original problem are studied. Finally, using method of estimate inequalities, the structure of solutions for the problem is discussed thoroughly in three cases and asymptotic solution of the original problem is given. The asymptotic behavior of solution in the three cases is proved.
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Foundation item: Supported by the National Natural Science Foundation of China (40676016 and 10471039), the National Program for Basic Science Researches of China (2003CB415101-03 and 2004CB418304), the Key Project of the Chinese Academy of Sciences (KZCX3-SW-221) and E-Insitutes of Shanghai Municipal Education Commission (N.E03004)
Biography: CHEN Lihua (1962–), female, Associate professor, research direction: nonlinear problems.
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Chen, L. A class of nonlinear nonlocal singularly perturbed reaction diffusion systems. Wuhan Univ. J. Nat. Sci. 13, 9–13 (2008). https://doi.org/10.1007/s11859-008-0103-7
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DOI: https://doi.org/10.1007/s11859-008-0103-7