Solution Dependence on Problem Type, Medium Parameters, and Initial Data

Abstract

Below, we considered a number of dynamic systems described by both ordinary and partial differential equations. Many applications concerning research of statistical characteristics of the solutions to these equations require the knowledge of the solution dependence (generally, in the functional form) on the medium parameters appeared in the equation as coefficients and initial values. Some properties appear common of all such dependencies, and two of them are of special interest in the context of statistical descriptions.