Acta mathematica scientia,Series B ›› 2016, Vol. 36 ›› Issue (6): 1651-1661.doi: 10.1016/S0252-9602(16)30097-2

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EXISTENCE OF WEAK SOLUTIONS FOR SOME SINGULAR PARABOLIC EQUATION

Li XIA1, Jingna LI2, Qiang LIU3   

  1. 1. College of Mathematics and Statistics, Guangdong University of Economics and Finance, Guangzhou 510320, China;
    2. Department of Mathematics, Jinan University, Guangzhou 510632, China;
    3. College of Mathematics and Computational Science, Shenzhen University, Shenzhen 518060, China
  • Received:2015-06-25 Revised:2016-05-09 Online:2016-12-25 Published:2016-12-25
  • Contact: Qiang LIU,E-mail:matliu@126.com E-mail:matliu@126.com
  • Supported by:

    This work was partially supported by NSFC (11201311, 11201181, 11301345), NSF of Guangdong Province (2015A030313623, 2016A030313048), Department of Education of Guangdong Province (YQ2015077, YQ2015020) and Shenzhen supporting scheme (ZYC201105130121A).

Abstract:

In this paper, we are concerned with a singular parabolic equation subject to Dirichlet boundary condition and initial condition. Under different assumptions on μ, ν and ψ, some existence results are obtained by applying parabolic regularization method and the sub-super solutions method.

Key words: existence, singular equation, blowup

CLC Number: 

  • 35K15
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