Study On The Extinction Properties Of Solutions For Two Types Of Parabolic Equations (groups)

In this paper, we investigate the quenching behavior of solutions for two quasilin-ear parabolic problems, including the quenching time, quenching point and quenching rate etc.In chapter 1, we study the quenching phenomenon of solutions for a quasilinear parabolic equation with singular boundary flux (?),where p, h, q are positive constants and p? 2, f(u) is a monotone decreasing function with f(u)>0 for u > 0. In addition, 0 < u0(x) < 1 and u0 satisfies the compatibil-ity conditions. By using some suitable auxiliary functions and the maximal principle technique, we prove that the solution must quench in finite time and the only quench-ing point is x = 0 with proper initial data. Then we established the upper and lower bound of the corresponding quenching rate.In chapter 2, we consider the quenching property of solutions for coupled heat equations with multi-nonlinearities (?)where p1,q2 ? 0,q1,p2 > 0 and we assume that the initial data u0,v0> 0 are smooth and compatible with the boundary data.By using the classic theory of parabolic equation and integral inequality technique , we will get a perfect standard to distinguish whether to simultaneous quenching and estimate the upper and lower bound of quenching rate.