Journal of Shanghai Jiaotong University ›› 2012, Vol. 46 ›› Issue (09): 1534-1538.

• Mathematics • Previous Articles    

Theoretical Analysis of a Nonlinear Parabolic Equation with TimeDelay

 WU  Hui-Ling   

  1. (Education College, Lishui University, Lishui 323000, China)
  • Received:2011-12-26 Online:2012-09-28 Published:2012-09-28

Abstract: Based on the denoising problem in image processing,the well-posedness of the initial-boundary value problem for a nonlinear parabolic equation with time-delay and a nonlocal term was studied.By using energy estimates and the fixed point theorem,the existence,uniqueness and stability of the weak solution to this initial-boundary problem were investigated.This study is helpful for the numerical simulation in image processing.  

Key words: nonlinear parabolic equation, timedelay, a nonlocal term, wellposedness, image processing