本文選題：粘彈性波方程　切入點：非線性阻尼　出處：《蘭州大學(xué)》2017年碩士論文

【摘要】：波方程在偏微分方程中具有十分重要的作用,對它的研究必將促進偏微分方程理論的進一步發(fā)展,而含記憶項的粘彈性波方程是波方程的重要內(nèi)容,本文研究如下非線性粘彈性波方程.其中?是Rn中的一個有界區(qū)域,并且具有光滑的邊界??,m2,松弛函數(shù)g:R+→R+是一個單調(diào)遞減且為正的函數(shù),p是一個常數(shù)滿足2p+∞,n=1,2,2p2(n-1)/n-2,n≥3.ρ也是一個常數(shù)滿足0ρ+∞,n=1,2,2ρ2/n-2,n≥3.在此文章中我們證明了在初始能量為任意大的條件下,方程解的全局非存在,突破了初始正能量有界的條件限制,并且這一結(jié)果是新的.在初始能量有界的條件下,方程解的全局非存在,可以參考[18].
[Abstract]:Wave equation plays an important role in partial differential equation. The study of wave equation will promote the further development of the theory of partial differential equation, and the viscoelastic wave equation with memory term is the important content of wave equation. In this paper, the following nonlinear viscoelastic wave equations are studied. Is a bounded region in rn and has a smooth boundary? ? Relaxation function g: r. 鈫扲 is a monotone decreasing and positive function, p is a constant satisfying 2p 鈭，

本文編號：1680002