| 58 | 0 | 132 |
| 下载次数 | 被引频次 | 阅读次数 |
研究一类具阻尼非线性波动方程的初边值问题{utt-αuxxtt-uxx+βut+γuxxt=φ(ux)x+f(u)xx-g(u),x∈(0,1),t>0,u(0,t)=u(1,t)=0,t≥0,u(x,0)=u0(x),ut(x,0)=u1(x),x∈[0,1]}局部古典解和整体古典解的存在性和唯一性,其中,α,β>0,γ<0均为常数,u(x,t)为未知函数,φ(s),f(s)和g(s)为给定的非线性函数,u0(x)和u1(x)是给定的初值函数.
Abstract：The existence and the uniqueness of the local classical solution and the global classical solution for the following initial boundary value problem for a class of damped nonlinear wave equations of fourth order were studied: utt-αuxxtt-uxx+βut+γuxxt=φ(ux)x+ f(u)xx-g(u),x ∈(0,1),t > 0,u(0,t)=u(1,t)= 0,t≥0,u(x,0)=u0(x),ut(x,0)=u1(x),x ∈, where α,β>0,γ<0 were constants,u(x,t) denoted an unknown function,φ(s),f(s) and g(s) were given nonlinear functions,u0(x) and u1(x) were given initial value functions.
[1]Clarkson P A,Levegue R J,Saxton R.Solitary-wave interactions in elastic rods[J].Stud Appl Math,1986,75(2):95-122.
[2]朱位秋.弹性杆中的非线性波[J].固体力学学报,1980(2):247-253.
[3]Zhang Wei,Yang Guitong.Propagation of solitary waves in the nonlinear rods[J].Appl Math Mech,1986,7(7):571-581.
[4]张善元,庄蔚.非线性弹性杆中的应变弧波[J].力学学报,1988,20(1):58-66.
[5]Makhankov V G.Dynamics of classical solitons in nonintegrable systems[J].Physics Reports:Section C of Physics Letters,1978,35(1):1-128.
[6]Arévalo E,Gaididei Y,Mertens F G.Soliton dynamics in damped and forced Boussinesq equations[J].Eur Phys J B,2002,27(1):63-74.
[7]Liu Yue.Existence and blow up of solutions of a nonlinear Pochhammer-Chree equation[J].Indiana Univ Math J,1996,45(3):797-816.
[8]Chen Xiangying.Existence and nonexistence of global solutions for nonlinear evolution equation of fourth order[J].Appl Math,2001,16(3):251-258.
[9]Chen Guowang,Wang Shubin.Existence and nonexistence of global solutions for nonlinear hyperbolic equations of higher order[J].Comment Math Univ Carolin,1995,36(3):475-487.
[10]Chen Guowang,Wang Shubin.Existence and nonexistence of global solutions for the generalized IMBq equation[J].NonlinearAnalysis:TMA,1999,36(8):961-980.
[11]陈国旺,吕胜关.人口问题中广义三维Ginzburg-Landau模型方程的初边值问题[J].应用数学学报,2000,23(4):507-517.
基本信息:
中图分类号:O175.8
引用信息:
[1]高慧敏,陈翔英.一类四阶具阻尼非线性波动方程的初边值问题[J],2011,43(04):19-27.
基金信息:
国家自然科学基金资助项目,编号10971199;; 河南省教育厅自然科学基金资助项目,编号2009C110006