具非线性扩散系数的偏微分方程组解的振动性  

Oscillation of Solutions to Systems of Partial Differential Equations with Nonlinear Diffusion Coefficient

作　　者：曾云辉[1] 

机构地区：[1]衡阳师范学院数学与计算科学系,湖南衡阳421008

出　　处：《重庆师范大学学报（自然科学版）》2010年第3期44-47,共4页Journal of Chongqing Normal University:Natural Science

基　　金：湖南省教育厅基金资助项目(No.07C165);衡阳师范学院科学基金项目(No.08A26)

摘　　要：考虑一类具非线性扩散系数的时滞双曲型偏微分方程组解的振动性,利用Green公式和边值条件将这类具非线性扩散系数的时滞双曲型偏微分方程组的振动问题转化为微分不等式不存在最终正解,通过利用Riccati变换和微分不等式方法,获得了该方程组在Robin边值条件ui(x,t)/N=0,(x,t)∈Ω×R+,i∈Im下所有解振动的充分条件是∫t0∞φ(s)Q(s)-4(s[)(1′(-s)σ]′2(s))ds=∞。In this paper, we studied the oscillation of solutions to systems of delay hyperbolic Partial differential equations with nonlinear diffusion coefficient. The oscillatory problem of solution to the systems of hyperbolic partial differential equations with nonlinear diffusion coefficient is reduced to which differential inequality has not eventual positive solution by using the Green＇s formula and boundaryvalue conditions. Thereby, sufficient condition∫t0 ∞{Ф（s）Q（s）-[Ф′（s）]^2/4Ф（s）（1-σ′（s））}ds=∞ for each solution to be oscillation is ob-tained under Robin boundary value condition δui（x,t）/δN=0,（x,t）∈δΩ×R.,i∈Im by using Riccati transformation and the method ofdiferential inequality.

关 键 词：振动 非线性扩散系数 RICCATI变换 

分 类 号：O175.23[理学—数学]