非线性边界输入下－维热传导方程解的存在唯一性

THE EXISTING UNIQUENESS OF ONE-DIMENSION HEAT CONDUCTION EQUATION SOLUTION UNDER THE INPUT OF NONLINEAR BOUNDARY

讨论了长度为ｌ＞０的一维均匀金属棒端．点在热辐射下的加热过程，其数学描述为状态空间Ｚ＝Ｃ［０，ｌ］中的非线性积分方程．证明了在［０，＋∞］上解的存在唯一性、解映射的局部Ｌｉｐｓｃｈｉｔｚ连续性以及局部紧性．

The heating process of one-dimension even metal bar whose length is l>0 is discussed. The non-linear integral equation is described to be the Space State x=C[0,l] by mathermatical method. The existing uniqueness,the part Lipschitz continuity of solution shine upon and the part tight of solution in [0, +∞].