Bounds for the Blow-up Time and Blow-up Rate Estimates for Nonlinear Parabolic Equations with Dirichlet or Neumann Boundary Conditions
Yuhua Jian
Department of Mathematics, School of Mathematics Science, Nanjing Normal University, Jiangsu Nanjing 210023, China.
Zuodong Yang *
Department of Mathematics, School of Mathematics Science, Nanjing Normal University, Jiangsu Nanjing 210023, China and College of Teacher Education, Nanjing Normal University, Jiangsu Nanjing 210097, China.
*Author to whom correspondence should be addressed.
Abstract
This paper is concerned with the blow-up phenomena for a type of parabolic equations with
weighted nonlinear source
where Ω ⊂ RN (N ≥ 3) is a smooth bounded domain. Through constructing some suitable auxiliary functions and using the rst-order di erential inequality technique, we obtain the bounds for the blow-up time and the estimates of the blow-up rate of the solution to the problem.
Keywords: Parabolic equation, bounds of blow-up time, estimates of blow-up rate, weighted nonlinear source.