| 摘要: |
| 利用Green定理和微分不等式,研究一类拟线性抛物型偏微分方程组:(∂ui(x,t)/∂t)=ai(t)Δui(x,t)+∑k=1s aik(t)Δui(x,dk(t))-pi(x,t)ui(x,t)-∑j=1m fij[t,x,uj(x,e(t))],i=1,2,…,m解的振动性,获得该类方程组在两类不同边值条件:(∂ui(x,t)/∂N)+gi(x,t)ui(x,t)=0,(x,t)∈∂Ω×R+,i=1,2,…,m和ui(x,t)=0,(x,t)∈∂K×R+,i=1,2,…,m所有解振动的若干充分条件:limt→∞ inf∫e(t)t q(s) exp∫e(s)s p(r) drds > 1/e. |
| 关键词: 微分方程 偏微分方程 拟线性 振动性 |
| DOI： |
| 投稿时间：2005-03-10 |
| 基金项目: |
|
| Oscillation for Solutions of Systems of Quasilinear Parabolic Partial Differential Equations |
|
Luo Liping
|
| (Department of Mathematics, Hengyang Normal University, Hengyang, Hunan, 421008, China) |
| Abstract: |
| The oscillation of solutions of the systems of a class of quasilinear parabolic partial differential equations:(∂ui(x,t)/∂t)=ai(t)Δui(x,t)+∑k=1s aik(t)Δui(x,dk(t))-pi(x,t)ui(x,t)-∑j=1m fij[t,x,uj(x,e(t))],i=1,2,…,m is studied by Green's theorem and differential inequalities.The sufficient conditions:limt→∞ inf∫e(t)t q(s) exp∫e(s)s p(r) drds > 1/e.for the oscillation of all solutions of the systems are obtained under two kinds of different boundary conditions:(∂ui(x,t)/∂N)+gi(x,t)ui(x,t)=0,(x,t)∈∂Ω×R+,i=1,2,…,m and ui(x,t)=0,(x,t)∈∂K×R+,i=1,2,…,m. |
| Key words: differential equation partial differential equation quasilinear oscillation |
