一类半线性热传导方程柯西问题整体解存在的唯一性  

Existence and Uniqueness for Global Solution of Cauchy Problem of a Class of Semilinear Heat Conduction Equation

作　　者：赵新俊[1] 孙萍[2] 

机构地区：[1]石河子大学师范学院数学系,新疆石河子832003 [2]乌鲁木齐职业大学,新疆乌鲁木齐830002

出　　处：《石河子大学学报（自然科学版）》2008年第2期253-256,共4页Journal of Shihezi University(Natural Science)

摘　　要：本文讨论了一类半线性热传导方程柯西问题整体解的存在唯一性。当初值φ和非线性项up(1-u)满足一定条件时,利用衰减估计和能量估计相结合的方法,并由Banach不动点定理得到了整体解的存在唯一性。The existence and uniqueness of the global solution of Cauchy problem for a class of semi-linear heat conduction equation are discussed in this paper. Utilizing the estimation of energy and the estimation of degeneration together, and by the Banach fixed point theorem, the existence and uniqueness of the global solution are presented, as the initial valueand the non-linear term u^P（ 1 - u） satisfy certain conditions.

关 键 词：半线性柯西问题 能量衰减 能量估计 不动点定理 

分 类 号：O175.26[理学—数学]