【摘要】 本文研究具非线性强耗散项的方程u_tt-γu_xx-β(u_xtx=f（x,t）及相应方程组在有界域与半无界域上的初边值问题,周期问题及初值问题,其中γ为任意常数。假设β∈C¹,β¹（s）≥α>0,f及初始函数满足一定条件,得到整体强解的存在与唯一性,进而,假设f=0,β及初始函数满足一定光滑条件,得到了强解的光滑性。更多还原

【Abstract】 In this paper the author considers the initial-boundary value problem in a finite and semi-infinite interval, the periodic problem and the initial value problem of the equation with nonlinear strong dissipation, utt-ruxx-βS(uxt)x= f(x,t), and the corresponding system, where y is an arbitrary constant. Suppose that β∈C1,β1(s)≥α>0 f and initial functions satisfy some conditions, we obtain the existence and the uniqueness of the global strong solution. Furthermore, suppose that f=0, β and initial functions satisfy some smoothing conditions, we obtain the smoothness of the strong solution.更多还原