方程u_(tt)-Δu-Δu_(tt)=f(x)的整体广义解  

Global generalized solutions of equation u_(tt)-Δu-Δu_t-Δu_(tt)=f(x)

作　　者：刘亚成[1] 徐润章[1] 

机构地区：[1]哈尔滨工程大学理学院,黑龙江哈尔滨150001

出　　处：《哈尔滨工程大学学报》2005年第3期406-408,共3页Journal of Harbin Engineering University

基　　金：国家自然科学基金资助项目(10271034);哈尔滨工程大学基础研究基金资助项目(HEU04012);哈尔滨工程大学学生科研立项资助项目(重点型ZE01).

摘　　要：研究四阶色散、耗散非线性波动方程的初边值问题utt-Δu-Δut-Δutt=f(x),x∈Ω,t>0,u(x,0)=u0(x),ut(x,0)=u1(x),x∈Ω,u| Ω=0,其中Ω∈RN为有界域.证明了如果f′(s)≤C0且对于N≥2存在p≥2及正常数A,B,A1及B1使得Asp-1-B≤f1(s)≤A1sp-1+B1,其中f1(s)=f(s)-k0s-f(0),k0=max{c0,0},u0(x)∈H10(Ω)∩Lq(Ω),u1(x)∈H10(Ω)则对任意T>0问题存在唯一解u(x,t)∈W1,∞0,T;H10(Ω)∩L∞(0,T;Lq(Ω)).<Abstrcat>A study was done on the initial boundary value problem of fourth order nonlinear wave equation with dispersive and dissipation term u_(tt)-Δu-Δu_t-Δu_u=f(x),x∈Ω,t>0,u(x,0)=u_0(x),u_t(x,0)=u_1(x),x∈Ω,((u｜_(Ω))=0), where Ω∈R^Nis a boundary domain. It is proved that if f′(s)≤C_0 and for N≥2 there exist p≥2 and positive constants A,B,A_1 and B_1 such that As^(p-1)-B≤f_1(s)≤A_1s^(p-1)+B_1, where f_1(s)=f(s)-(k_0s-f(0)),k_0=max｛c_0,0｝,u_0(x)∈H^1_0(Ω)∩L^q(Ω),u_1(x)∈H^1_0(Ω),then for any T>0 the problem (admits a) unique solution u(x,t)∈W^(1,∞)0,T;H^1_0(Ω)∩L~∞(0,T;L^q(Ω)).

关 键 词：非线性波动方程 色散 耗散 整体广义解 

分 类 号：O175.26[理学—数学]