MODELING DYNAMIC PROCESSES IN LANDSCAPE-DISCRETE DOMAINS BY THE METHOD OF CONTRAST STRUCTURES WITH LIMIT STATES

Contrast structures are functions whose domains contain subdomains in which these functions have large gradients. These subdomains are called internal transition layers. The width of the transition layer is typically much smaller than the width of the domain under consideration; therefore, in problems with solutions in the form of contrast structures, it is always possible to identify a small parameter. Problems with a small parameter can be analyzed analytically using asymptotic methods. In particular, the method of differential inequalities allows one to obtain conditions for the existence of solutions in the form of contrast structures and for the stability of stationary contrast structures. These conditions were taken into account when developing mathematical models of the following phenomena: 1) air flow around heterogeneous vegetation (small forest areas), 2) a microscopic model of rock destruction during CO2 injection, 3) a model of tumor spheroid growth.