半线性方程强弱余法奇性波的相互干扰

半线性方程强弱余法奇性波的相互干扰 TRANSVERSAL INTERACTION CONORMAL OF WAVES WITH STRONG AND WEAK SINGULARITIES FOR SIMI-LINEAR EQUATIONS 沈未名 1 first-author 王维克 1 武汉大学数学系 武汉大学数学系 Department of Mathematics,Wuhan University Department of Mathematics,Wuhan University 首先定义并考查了一类新的函数空间，即所谓二重余法分布．在得到了一些建立在此类余法分布空间上的能量估计之后，证明了半线性严格双曲的一阶偏微分方程组的弱奇性与强奇性相互作用后将会产生透射与反射等新奇性，而且其强度不强于原弱奇性的强度． This paper discusses the transversal interaction of two differential strength conormal singularities-strong and weak. For escaping from difficulties of "Paralinearization"with discontinuous solution, we use a method of iteration.So we define a kind of mew func tion space, called twice conormal distribution,in order to discribe the case of some singularities over another kind of singularities.With some estimates on these function space,we can get the main result of this paper as following:after inreraction,some mew singularites willtake place and their strength will be not more than the original weak one. 半线性偏微分方程 余法分布空间 非线性波 能量估计 simi-linear partial differential equation conormal distribution nonlinear wave energy estimate. O175.2 国家自然科学基金,国家教委留学回国人员基金 1994-04-01 2021-04-01 4