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

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.