Finite Time Blow-up, Extinction and Non-extinction of Solutions for an Evolutionary Problem
Zhen Zhi
Institute of Mathematics, School of Mathematics Science, Nanjing Normal University, Jiangsu Nanjing 210023, China.
Zuodong Yang *
Institute of Mathematics, School of Mathematics Science, Nanjing Normal University, Jiangsu Nanjing 210023, China and School of Teacher Education, Nanjing Normal University, Jiangsu Nanjing 210097, China.
*Author to whom correspondence should be addressed.
Abstract
In this paper we consider a class of p-biharmonic parabolic equation with nonlocal nonlinearities and Neumann boundary condition. By constructing suitable auxiliary functions and using differential inequalities, we give blow-up criterion of solutions as well as extinction and nonextinction.
In addition, we derive similar results for a different equation.
Keywords: p-biharmonic parabolic equation, blow-up, extinction