非线性拟抛物型积分微分方程的初边值问题和初值问题

Initial Boundary Value Problem and Initial Value Problem for the Nonlinear Integrodifferential Equations of Pseudoparabolic Type

本文研究非线性拟抛物型积分微分方程的初边值问题和初值问题 .运用Galerkin方程结合能量估计证明了问题的整体强解的存在性、唯一性和稳定性 ,最后在一定条件下讨论了初边值问题整体解的不存在性和爆破问题 .

This paper studies the initial boundary value problem and initial value problem for the nonlinear integrodifferential equations of pesudo-parabolic type. The existence, uniqueness, and stability of the global strongly solution of the problem are proved by combining the Galerkin method and a priori estimates, and the nonexistence of global solutions and blow up problem are also discussed under certain conditions