GLOBAL EXISTENCE AND BLOW-UP OF SOLUTIONS FOR GENERALIZED POCHHAMMER-CHREE EQUATIONS  

作　　者：徐润章 刘亚成 

机构地区：[1]College of Science,Harbin Engineering University

出　　处：《Acta Mathematica Scientia》2010年第5期1793-1807,共15页数学物理学报（B辑英文版）

基　　金：supported by National Natural Science Foundation of China(10871055,10926149);Natural Science Foundation of Heilongjiang Province (A2007-02;A200810);Science and Technology Foundation of Education Office of Heilongjiang Province(11541276);Foundational Science Founda-tion of Harbin Engineering University

摘　　要：In this article, we study the initial boundary value problem of generalized Pochhammer-Chree equation utt-uxx-uxxt-uxxtt=f（u）xx,x∈Ω,t〉0,u（x,0）=u0（x）,ut（x,0）=u1（x）,x∈Ω,u（0,t）=u（1,t）=0,t≥0, where Ω = （0, 1）. First, we obtain the existence of local Wkp solutions. Then, we prove that, if f（s） ∈ Ck＋1（R） is nondecreasing, f（0） = 0 and ｜f（u）｜ ≤ C1｜u｜∫0uf（s）ds ＋ C2, u0（x）,u1（x） ∈ WkP（Ω） ∩ W01,P（Ω）, k≥ 1, 1 〈 p≤ ∞, then for any T 〉 0 the problem admits a unique solution u（x, t） ∈ W2,∞（0, T; WkP（Ω） ∩ W01,P（Ω））. Finally, the finite time blow-up of solutions and global Wkp solution of generalized IMBo equations are discussed.In this article, we study the initial boundary value problem of generalized Pochhammer-Chree equation utt-uxx-uxxt-uxxtt=f（u）xx,x∈Ω,t〉0,u（x,0）=u0（x）,ut（x,0）=u1（x）,x∈Ω,u（0,t）=u（1,t）=0,t≥0, where Ω = （0, 1）. First, we obtain the existence of local Wkp solutions. Then, we prove that, if f（s） ∈ Ck＋1（R） is nondecreasing, f（0） = 0 and ｜f（u）｜ ≤ C1｜u｜∫0uf（s）ds ＋ C2, u0（x）,u1（x） ∈ WkP（Ω） ∩ W01,P（Ω）, k≥ 1, 1 〈 p≤ ∞, then for any T 〉 0 the problem admits a unique solution u（x, t） ∈ W2,∞（0, T; WkP（Ω） ∩ W01,P（Ω））. Finally, the finite time blow-up of solutions and global Wkp solution of generalized IMBo equations are discussed.

关 键 词：Pochhammer-Chree equations initial boundary value problem Wkp solu-tion global existence BLOW-UP 

分 类 号：O175.8[理学—数学]