一类半线性热方程组的非负非平凡解(英文)

Nontrivial Nonnegative Solutions of a Class of Semi-Linear Heat Equations System

利用算子半群理论和几个不等式讨论了一类半线性热方程组初值问题的非负非平凡解,验证了方程组(1)的非负非平凡解具有有界性的结果,并进一步得出其上下界的具体形式,从而得到了方程组(1)在(0,T)×Rn上的非负非平凡解.

By using of the theory of semi-group operators and several inequalities, the nonwivial nonnegative so- lutions of initial value problem of semi-linear heat equations are studied. It is verified that the nontrivial nonnega- tive solution of the equations （ 1 ） is bounded. The concrete form of its upper and lower bounds are then gained. Thus, the nonnegative nontrivial solutions of the equations （1） in （0, T）× Rn are obtained.