Аннотации:
Nonlinear diffusion equation and Liesegang rings are studied. It is assumed that there exists a finite number of continuous curves such that different curves can have common points only at the endpoints. There exist one-sided derivatives on the curves and oppositely signed values on different sides also exist. An asymptotic expansion of the solution in this neighborhood is sought in the form of the series is constructed. Since the solution of the problem is even, only positive values of x are considered. To determine the leading term of asymptotic expansion, the solutions of the homogeneous equation are found. The conditions imposed on the initial function imply that the function decreases and, at some time, u(0, t) reaches the value a.