Abstract
A lot of processes coming from Physics, Chemistry, Biology, Economy, and other sciences can be described using systems of reaction-diffusion equations. In this chapter, we study the asymptotic behavior of the solutions of a system of infinite ordinary differential equations (a lattice dynamical system) obtained after the spacial discretization of a system of reaction-diffusion equations in an unbounded domain. This kind of dynamical systems is then of importance in the numerical approximations of physical problems.
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Zgurovsky, M.Z., Kasyanov, P.O., Kapustyan, O.V., Valero, J., Zadoianchuk, N.V. (2012). Attractors for Lattice Dynamical Systems. In: Evolution Inclusions and Variation Inequalities for Earth Data Processing III. Advances in Mechanics and Mathematics, vol 27. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-28512-7_3
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