非局部反应扩散方程的一致爆破速率

Uniform Blow-up Rates for Diffusion Equations with Nonlocal Source

该文研究了带有非局部源的扩散方程的爆破速率．关于这类方程,作者证得该类方程的解整体爆破且其爆破速率在区域的任一紧子区域内是一致的．在各种情形下,当t趋向于爆破时刻T*时,|u(t)|∞的爆破速率可精确确定．

In this paper, the author investigates the rates of blow-up of solutions of diffusion equations with nonlocal nonlinear reaction terms. For large classes of equations, the author proves that the solutions have global blow-up and that the rate of blow-up is uniform in all compact subsets of the domain. In each case, the blow-up rate of ｜u（t）｜∞ is precisely determined as t approaches the blow-up time T^＊.