Solvability of a boundary value problem of chaotic dynamics of polymer molecule in the case of bounded interaction potential

This paper deals with a boundary value problem for a parabolic differential equation that describes a chaotic motion of a polymer chain in water. The equation is nonlocal in time as well as in space. It includes a so called interaction potential that depends on the integrals of the solution over the entire time interval and over the space domain where the problem is being solved. The time nonlocality appears since the time plays the role of the arc length along the chain and each segment interacts with all others through the surrounding fluid. The weak solvability of the problem is proven for the case of the bounded continuous interaction potential. The proof of the solvability does not use any continuity properties of the solution with respect to the time and is based on the energy estimate only.