一类非线性积分微分方程解及其构造

THE SOLUTION AND ITS CONSTRUCTION FOR A CLASS OF NONLINEAR INTEGRO-DIFFERENTIAL EQUATIONS

本文讨论了核反应堆动力学中一类具缓发中子的非线性积分微分方程．在一定的条件下证明了该方程在p空间中Mild解、强解、局部解的存在唯一性，以及用迭代法求解的合理性，并估计了收敛速度．

This paper discusses a class of nonlinear integro-differential equations arising in nuclear reactor dynamics. Under certain conditions the existence and uniqueness of Mild solution, strong solution and local solution are proved. It also shows that the solution can be obtained by the iterative method. Moreover, the convergence speed of this method is estimated.