摘要
设ｕ（ｔ，ｘ），ｕ（ｔ，ｘ）为初值问题在带形域ＳＴ＝（０，Ｔ）×Ｒｎ内的两个非负经曲解，ｆ（ｘ）连续有界非负的实函数，则有如下的结果：（１）若ｆ（ｘ）不恒为零，则在ＳＴ中ｕ（ｔ，ｘ）；（２）若γ＞１，则在ＳＴ中ｕ（ｔ，ｘ）ｕ（ｔ，ｘ）；（３）若０＞γ＞１，ｆ（ｘ）０，则问题（１．１），（１．２）的解不唯一且它的所有非平凡解的集合为ｕ（ｔ，ｓ）＝这里ｓ≥０是参数，其中记号（γ）＋＝ｍａｘ｛γ，０｝．
Let u(x, t), u(t, x) be two nonnegative classical solution in ST = (0, T)× Rn for the following initial problem where f(x) is a continuous, bounded and nonnegative real function. Then we have the following results: (1) If f(x) is not identically equal to zero, then u(t, x) = u(t, x) in ST; (2) Ifγ> 1, then u(t,x) = u(t,x) in ST, (3) If 0 <γ< 1, f(x) 0 then the solution for (1.1), (1.2) is not unique, and the whole set of all nontrivial solutions is u(t, s) = where is a parameter, Sign = max {γ, 0}.
出处
《数学学报（中文版）》
SCIE
CSCD
北大核心
2000年第2期301-308,共8页
Acta Mathematica Sinica：Chinese Series
基金
云南省教委青年基金
关键词
奇异半线性热方程
算子半群
唯一性
初值问题
解
Singular semilinesr heat equation
Semigrap of operator, Uniqueness of solution
