具有非线性范数型源的反应扩散方程组解的爆破性质

BLOW-UP PROPERTIES FOR A REACTION-DIFFUSION SYSTEM WITH NONLINEAR NORM-TYPE SOURCES

本文研究了一类带有非线性范数型源的反应扩散方程组u_t=?u^m+a‖u^(p1)v^(q1)‖_α^(r1),v_t=?v^n+b‖v^(p2)w^(q2)‖_β^(r2),w_t=?w^h+c‖w^(p3)u^(q3)‖_γ^(r3)在齐次Dirichlet边界条件下解的爆破问题.利用上下解方法和构造辅助函数的技巧,得到了方程组解的整体存在与爆破的准则,将当前的一些研究结果推广到更复杂的情形.

In this paper, we study the blow-up problems for a class of reaction-diffusion system with nonlinear norm-type sources：ut=△um＋a‖u（p1）v（q1）‖α（r1）,vt=△vn＋b‖v（p2）w（q2）‖β（r2）,wt=△wh＋c‖w（p3）u（q3）‖γ（r3） subject to homogeneous Dirichlet conditions. By using upper-lower solution method and constructing auxiliary functions＇ techniques, we obtain the criteria for global existence or finite time blow-up, which extend some results of the current research to more complex situations.