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Global well-posedness of coupled parabolic systems

  • Runzhang XuEmail author
  • Wei Lian
  • Yi Niu
Articles
  • 12 Downloads

Abstract

The initial boundary value problem of a class of reaction-diffusion systems (coupled parabolic systems) with nonlinear coupled source terms is considered in order to classify the initial data for the global existence, finite time blowup and long time decay of the solution. The whole study is conducted by considering three cases according to initial energy: the low initial energy case, critical initial energy case and high initial energy case. For the low initial energy case and critical initial energy case the suffcient initial conditions of global existence, long time decay and finite time blowup are given to show a sharp-like condition. In addition, for the high initial energy case the possibility of both global existence and finite time blowup is proved first, and then some suffcient initial conditions of finite time blowup and global existence are obtained, respectively.

Keywords

reaction-diffusion systems coupled parabolic systems global existence asymptotic behavior finite time blowup 

MSC(2010)

35K51 35K40 

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Notes

Acknowledgements

This work was supported by National Natural Science Foundation of China (Grant No. 11471087), the China Postdoctoral Science Foundation International Postdoctoral Exchange Fellowship Program, the Heilongjiang Postdoctoral Foundation (Grant No. LBH-Z13056) and the Fundamental Research Funds for the Central Universities. Part of this work was finished when the first author visited Professor Zhouping Xin in the Institute of Mathematical Sciences, the Chinese University of Hong Kong. The authors appreciate the referees' valuable suggestions, which help so much with the improving and modification of this paper. Thanks are also to Dr. Xingchang Wang and Dr. Yuxuan Chen for helping revise the paper.

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Copyright information

© Science China Press and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.College of AutomationHarbin Engineering UniversityHarbinChina
  2. 2.College of ScienceHarbin Engineering UniversityHarbinChina
  3. 3.The Institute of Mathematical SciencesThe Chinese University of Hong KongHong KongChina
  4. 4.School of Information Science and EngineeringShandong Normal UniversityJinanChina

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