Global well-posedness of coupled parabolic systems
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 conduct...
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| Published in | Science China. Mathematics Vol. 63; no. 2; pp. 321 - 356 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
Beijing
Science China Press
01.02.2020
Springer Nature B.V |
| Subjects | |
| Online Access | Get full text |
| ISSN | 1674-7283 1869-1862 |
| DOI | 10.1007/s11425-017-9280-x |
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| 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. |
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| AbstractList | 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. |
| Author | Lian, Wei Xu, Runzhang Niu, Yi |
| Author_xml | – sequence: 1 givenname: Runzhang surname: Xu fullname: Xu, Runzhang email: xurunzh@163.com organization: College of Automation, Harbin Engineering University, College of Science, Harbin Engineering University, The Institute of Mathematical Sciences, The Chinese University of Hong Kong – sequence: 2 givenname: Wei surname: Lian fullname: Lian, Wei organization: College of Automation, Harbin Engineering University – sequence: 3 givenname: Yi surname: Niu fullname: Niu, Yi organization: College of Automation, Harbin Engineering University, School of Information Science and Engineering, Shandong Normal University |
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| SubjectTerms | Applications of Mathematics Boundary value problems Decay Energy Initial conditions Mathematical problems Mathematics Mathematics and Statistics Nonlinear systems Well posed problems |
| Title | Global well-posedness of coupled parabolic systems |
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