ИСТИНА

Within the framework of the two-dimensional spatial economy, various forms of urban structures are considered. Since the number of structurally stable urban configurations is rather limited, structurally unstable formations are of great interest. For example, there are city models that behave near unstable singular points like a «running» wave. In this paper we consider a system of quasi-linear parabolic equations for two unknown functions: population density and, so-called, quality of housing stock. After some transformations of the required functions and variables we seek a self-similar solution in the form of a running wave with an unknown amplitude and velocity. Further the stability of the obtained solution is analyzed. To determine the role of the obtained particular (self-similar) solution, the Cauchy problem for different initial conditions is also solved numerically. The results of computational experiments show us that the analytical wave-like solution can be interpreted is an intermediate asymptotic for the partial differential problem which is being considered this paper. Internet: https://icmsquare.net/