On the Solution of Boundary-Value Problems of Kolmogorov–Petrovskii–Piskunov Type

We describe a number of properties of solutions of boundary-value problems for nonlinear ordinary differential equations of the same type as those studied by Kolmogorov, Petrovskii, and Piskunov in their well-known paper on waves described by the parabolic equation. We construct and justify the asymptotics of such solutions for large values of the modulus of the independent variable.