Journal of Inequalities and Applications
Volume 6 (2001), Issue 1, Pages 57-75

Global and blowup solutions of quasilinear parabolic equation with critical Sobolev exponent and lower energy initial value

Zhong Tan1 and Zheng-An Yao2

1Department of Mathematics, Xiamen University, Fujian, Xiamen 361005, China
2Department of Mathematics, Zhongshan University, Guangdong, Guangzhou 510275, China

Received 25 August 1999; Revised 22 October 1999

Copyright © 2001 Zhong Tan and Zheng-An Yao. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


In this paper, by means of the energy method, we first study the existence and asymptotic estimates of global solution of quasilinear parabolic equations involving p-Laplacian (p>2) and critical Sobolev exponent and lower energy initial value in a bounded domain in RN(N3), and also study the sufficient conditions of finite time blowup of local solution by the classical concave method. Finally, we study the asymptotic behavior of any global solutions u(x,t;u0) which may possess high energy initial value function u0(x). We can prove that there exists a time subsequence {tn} such that the asymptotic behavior of u(x,tn;u0) as tn is similar to the Palais–Smale sequence of stationary equation of the above parabolic problem.