Journal of Shanghai University(Natural Science Edition) ›› 2014, Vol. 20 ›› Issue (6): 741-748.

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Existence of Solutions for an Initial Control Problem with Dynamic Boundary Conditions

TONG Chun1,2, WANG Yuan-di1   

  1. 1. College of Sciences, Shanghai University, Shanghai 200444, China;2. Department of Public Teaching, Ningbo Polytechnic, Ningbo 315800, Zhejiang, China
  • Received:2013-11-17 Online:2014-12-23 Published:2014-12-23

Abstract: An initial control problem with dynamic boundary conditions is investigated by using a method of maximal principle. The comparison principle and existence of solutions for the control problem under some assumptions are proved. Some examples with multiple solutions and unique solution are gived.

Key words: boundary value problem;upper-lower solutions, control problem, maximal principle, nonlocal, parabolic equation

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