摘要
本文用 Galtrkin 方法和 Soboltv 型估计,研究了一类非线性拟抛物型方程.U_t—a_l(t)U_(xxt)—a_2(t)U_(xx)+f(x,t,U,U_x)的初值边值问题,周期边值问题和初值问题的古典解的存在性,唯一性和稳定性.
In this paper,Using Galerkin method and soboler estimates,we discuss the existence, uniqueness and stability of the classical solutions of the first initial-boundary value prob- lems and periodic-boundary problems and initial value problems for the nonlinear pseudo-parabolic equationsU_t-a_1(t)U_(xx(?))-a_2(t)U_(xx)=f(x,t,U,U_x)
关键词
拟抛物型方程
初边值
周期边值
pseudo-parabolic equation
initial-boundary problem
operator
