Abstract:
The asymptotic behaviour of equilibria that rapidly oscillate in the spatial coordinate in a system of two nonlinear parabolic equations with a sufficiently small diffusion coefficient in one of them is investigated. The normalization method is applied to show that the local dynamics of the original system with a small parameter multiplying one of the high-order derivatives is determined by the non-local behaviour of the solutions of a family of special boundary-value problems that are independent of the small parameter.
This publication is cited in the following 4 articles:
I Kashchenko, “The behavior of solutions of an equation with a large spatially distributed control”, J. Phys.: Conf. Ser., 937 (2017), 012021
D. V. Glazkov, “Lokalnaya dinamika uravneniya vtorogo poryadka s bolshim eksponentsialno raspredelennym zapazdyvaniem i suschestvennym treniem”, Model. i analiz inform. sistem, 22:1 (2015), 65–73
Kashchenko S.A., “Dynamics of a Spatially Distributed Logistic Equation with Small Diffusion and Small Delay”, Differ. Equ., 49:12 (2013), 1502–1510
S. A. Kashchenko, “Asymptotic form of spatially non-uniform structures in coherent nonlinear optical systems”, U.S.S.R. Comput. Math. Math. Phys., 31:3 (1991), 97–102