Solvability of a regularized boundary value problem of chaotic dynamics of a polymer molecule

Abstract

This paper deals with a parabolic partial differential equation that describes the chaotic dynamics of a polymer chain in water solution. This equation includes a non-linear nonlocal in time term and the integral of the solution over the space domain that stands in a denominator. For this reason, a regularized problem is considered. The regularization prevents vanishing this integral.
The weak solvability of the initial boundary value problem for this equation is proven.