论文标题
全局抛物线方程的边界价值问题
Boundary value problem for a global in time parabolic equation
论文作者
论文摘要
本文的目的是提请人们注意一个有趣的半线性抛物线方程，该方程描述了液体中聚合物分子的混沌动力学时会产生。该方程在时间上是非本地的，并且包含一个称为相互作用势的术语，该术语取决于解决问题的整个间隔中解决方案的时间集成量。实际上，需要了解“未来”才能确定本术语中的系数，即违反因果原则。证明了初始边界价值问题的弱解决方案的存在。相互作用的潜力满足了相当普遍的条件，并且可以在无穷大时具有任意增长。该解决方案的唯一性是根据考虑时间间隔的长度限制的。
The aim of this paper is to draw attention to an interesting semilinear parabolic equation that arose when describing the chaotic dynamics of a polymer molecule in a liquid. This equation is nonlocal in time and contains a term, called the interaction potential, that depends on the time-integral of the solution over the entire interval of solving the problem. In fact, one needs to know the "future" in order to determine the coefficient in this term, i.e., the causality principle is violated. The existence of a weak solution of the initial boundary value problem is proven. The interaction potential satisfies fairly general conditions and can have an arbitrary growth at infinity. The uniqueness of this solution is established with restrictions on the length of the considered time interval.
