一类多维非线性拟双曲方程的整体强解(Ⅱ)—初值问题

Global Strong solution for A Classof Nonlinear Pseudo-hyperbolic Equations in Multidimensions( Ⅱ ) -Initial Value Problem

本文在文[1]基础上,研究一类多维非线性拟双曲方程的初值问题 u,,一尸ut‘/(uc)+夕(x,f,u,尸“,uf,尸ut) (1) IJl,霹。二uo(X), ufl,.o二ul(X) (2)在f,g满足与[1]类似的条件下,证明了问题(1),(2)整体强解的存在与唯一性。

This paper study the initial boundary value problem for a class of multi-dimentional nonlinear pseudo-hyperbolic equationsby means of Galerkins method, suppose that f C1, f', are bounded from above, g|uf=0 and f (n>4), g satisfy certain growth conditions, obtain the existens and uniquness of global strong solution.