具混合边界的双曲微分方程在Lp(0,T;W1,p(Ω))空间中的研究
STUDY ON HYPERBOLIC DIFIERENTIAL EQUATION WITH MIXED BOUNDARIES

本文研究了一类具混合边界的一般形式的双曲微分方程.利用分裂方程和Neumann边界条件的方法，借助于定义非线性算子，并利用Reich关于极大单调算子值域几乎相等的结论检验所定义算子具备某些性质的技巧，获得了双曲边值问题在Lp（0，T；W1，p（Ω））空间中存在唯一解的结果.基于双曲方程中的主项是非线性的，所以本文应用了新的证明技巧，推广和补充了以往的相关工作.
In this paper, one kind of general form of hyperbolic differential equation with mixed boundaries is studied. By using the method of splitting the equation and the Neumann boundary condition respectively, and by defining some nonlinear operators and checking some properties of theirs in view of the result of almost equality of the ranges for maximal monotone operators presented by Reich, we prove that the hyperbolic boundary value problem has a unique solution in Lp(0,T;W1,p(Ω)). Some new techniques can be found since the main parts in the hyperbolic equation are nonlinear, which can be regarded as the complement and extension of the previous work