Global Existence and Blowup Analysis to Single-Species Bacillus System with Free Boundary
This paper is concerned with a reaction-diffusion equation which describes the dynamics of single bacillus population with free boundary. The local existence and uniqueness of the solution are first obtained by using the contraction mapping theorem. Then we exhibit an energy condition, involving the...
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| Format: | Article |
| Language: | English |
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Wiley
2011-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2011/326386 |
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| _version_ | 1832565386217783296 |
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| author | Zhi Ling Zhigui Lin |
| author_facet | Zhi Ling Zhigui Lin |
| author_sort | Zhi Ling |
| collection | DOAJ |
| description | This paper is concerned with a reaction-diffusion equation which describes the dynamics of single bacillus population with free boundary. The local existence and uniqueness of the solution are first obtained by using the contraction mapping theorem. Then we exhibit an energy condition, involving the initial data,
under which the solution blows up in finite time. Finally we examine the long time behavior of global solutions;
the global fast solution and slow solution are given. Our results show that blowup occurs if the death rate is small and
the initial value is large enough. If the initial value is small the solution is global and fast, which decays at an exponential rate while there is a global slow solution provided that the death rate is small and the initial value is suitably large. |
| format | Article |
| id | doaj-art-665680192ce2485b89652a1bcb53b6fa |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2011-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-665680192ce2485b89652a1bcb53b6fa2025-02-03T01:07:53ZengWileyAbstract and Applied Analysis1085-33751687-04092011-01-01201110.1155/2011/326386326386Global Existence and Blowup Analysis to Single-Species Bacillus System with Free BoundaryZhi Ling0Zhigui Lin1School of Mathematical Science, Yangzhou University, Yangzhou 225002, ChinaSchool of Mathematical Science, Yangzhou University, Yangzhou 225002, ChinaThis paper is concerned with a reaction-diffusion equation which describes the dynamics of single bacillus population with free boundary. The local existence and uniqueness of the solution are first obtained by using the contraction mapping theorem. Then we exhibit an energy condition, involving the initial data, under which the solution blows up in finite time. Finally we examine the long time behavior of global solutions; the global fast solution and slow solution are given. Our results show that blowup occurs if the death rate is small and the initial value is large enough. If the initial value is small the solution is global and fast, which decays at an exponential rate while there is a global slow solution provided that the death rate is small and the initial value is suitably large.http://dx.doi.org/10.1155/2011/326386 |
| spellingShingle | Zhi Ling Zhigui Lin Global Existence and Blowup Analysis to Single-Species Bacillus System with Free Boundary Abstract and Applied Analysis |
| title | Global Existence and Blowup Analysis to Single-Species Bacillus System with Free Boundary |
| title_full | Global Existence and Blowup Analysis to Single-Species Bacillus System with Free Boundary |
| title_fullStr | Global Existence and Blowup Analysis to Single-Species Bacillus System with Free Boundary |
| title_full_unstemmed | Global Existence and Blowup Analysis to Single-Species Bacillus System with Free Boundary |
| title_short | Global Existence and Blowup Analysis to Single-Species Bacillus System with Free Boundary |
| title_sort | global existence and blowup analysis to single species bacillus system with free boundary |
| url | http://dx.doi.org/10.1155/2011/326386 |
| work_keys_str_mv | AT zhiling globalexistenceandblowupanalysistosinglespeciesbacillussystemwithfreeboundary AT zhiguilin globalexistenceandblowupanalysistosinglespeciesbacillussystemwithfreeboundary |