关于非线性偏微分方程的特征曲面  

ON CHARACTERISTIC SURFACE OF NON-LINEAR PARTIAL DIFFERENTIAL EQUATIONS

作　　者：吴方同[1] 

机构地区：[1]武汉大学数学系,武汉430072

出　　处：《应用数学学报》1998年第3期353-358,共6页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金;国家教委博点基金

摘　　要：设,为m阶非线性偏微分方程F（x,u，…，D^au，…）＝0（｜a｜≤m）的实解，本文通过特征方法构造其特征曲面，并应用Bony[1]的奇性传播定理证明了特征曲面的正则性，从而获得对Alinhac[2]中条件的一个注记．Let u∈H(Ω) (ΩIR^n+1 s >) be a real solution of non-linearpartial differential equation F(x, u，… u,…)|α|≤m = O. In this paper, characteribticsurfaces of non-linear equation can be constructed by classical characteristic method. Andappling theorem[1] of propagation of singularities, the regularities of characteristic surfacescan be obtained. Finally we give a note which makes the condition of the theorem[2] can beadvanced.

关 键 词：特征曲面 零次特征 偏微分方程 非线性 

分 类 号：O175.29[理学—数学]