一类半线性热方程整体解的存在性与非存在性

Existence and Nonexistence of Global Solutions for a Class of Semilinear Heat Equations

本文研究半线性热方程的初值问题u_t－△u＝u~γ＋cu，（γ＞1）；u（x，0）=（x）非负整体L^P解的存在性与非存在性．首先证明，若C＞0，则不存在非负整体解．而后，对C＜0情形给出了解的整体存在与非存在的充分条件，特别证明了，若P＞（γ一1）或，则当。充分小时存在非负整体L^P解.最后，对系数C和初值（x）得到无穷多个门槛结果．

This paper studes the existence and nonexistence of nonnegative global LPsolutions for the initial value problem of semilinear heat equations ut -△u = uγ + cu,(γ＞ l), u(x, 0) = (x). First proves that if c ＞0 then there are no nonnegative globalsolutions. Next for the case c＜0 gives the sufficient conditions of global existence andnonexistence of solutions, in particular proves that if or ,then when is sufficiently small there exist nonnegative global LP solutions. Finallyobtains ifinit threshold results for the coefficient c and the initial data (x).