Nonlinear second order degenerate parabolic equation: existence theorem and exact solutions

The report concerns the study of a non-linear evolutionary second order parabolic equation with degeneration, which is a mathematical model of several physical and biological processes. We consider solutions having the form of a diffusion (thermal, filtration) wave that propagates over a zero background with a finite velocity. An existence and uniqueness theorems are proved in the class of piecewise analytical functions. We also obtain and study exact solutions, whose construction reduces to integrating of the Cauchy problem for an ordinary differential equation.