一类反应扩散系统解的整体有界性

Global boundedness of solutions to a class of reaction-diffusion systems

研究一类反应扩散系统解的整体有界性 .首先运用广义特征函数的方法证明了解在L1 意义下的整体有界性 ;由于新的特征函数在区域的边界上有非负下界 ,从而避免了经典特征函数在边界上为零的缺陷 .然后从解的 L1 整体有界性出发 ,进一步得到解在 L∞

This paper deals with the global existence of solutions to a class of reaction diffusion system. At first, the global L1 boundedness of solutions is established by using a new generalized eigenfunction method, since the new eigenfunction has nonnegative lower bound rather than zero on Ω, so the new method is more useful than the classical one. Then the L∞ boundedness of solutions is obtained on the basis of the L1 boundedness.