Problem of chaotic dynamics of polymer chain with a partly bounded interaction potential

The paper deals with a parabolic boundary value problem that describes the chaotic dynamics of a single polymer chain in a liquid. The time in the parabolic equation plays the role of the arc length parameter along the chain and corresponds to the link number. The equation includes a so called interaction (between the links) potential that has a double non-locality. It depends on the integrals of the solution over the entire time interval and over the entire space domain where the problem is being solved. Moreover, the space non-locality is in a denominator, which causes additional difficulties related to the possible vanishing of the integral. It is managed to prove that this integral does not vanish, if the interaction potential is bounded on an open part of the domain. This part can be very small, but not empty. This condition implies that the potential is a function of two variables. The first one is the space variable and the second depends on the solution. With respect to the second variable, the potential satisfies fairly general conditions and can be a bounded from below continuous function with an arbitrary growth at infinity, which entails that the interaction term is not a lower order term in the equation. The existence of a weak solution of the initial boundary value problem is proven.