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Development of the asymptotic method of differential inequalities for investigation of periodic contrast structures in reaction-diffusion equations. (Russian, English) Zbl 1210.35155
Zh. Vychisl. Mat. Mat. Fiz. 46, No. 4, 615-623 (2006); translation in Comput. Math. Math. Phys. 46, No. 4, 585-593 (2006).
Summary: The asymptotical method of differential inequalities is developed for a new class of periodic problems of reaction-diffusion type. The problem of the existence and Lyapunov stability of periodic solutions with internal transient layers in the case of balanced nonlinearity is studied.

MSC:
35K57 Reaction-diffusion equations
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