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Global Existence and Blowup Analysis to Single‐Species Bacillus System with Free Boundary

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  • Zhi Ling
  • Zhigui Lin

Abstract

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.

Suggested Citation

  • Zhi Ling & Zhigui Lin, 2011. "Global Existence and Blowup Analysis to Single‐Species Bacillus System with Free Boundary," Abstract and Applied Analysis, John Wiley & Sons, vol. 2011(1).
    • Handle: RePEc:wly:jnlaaa:v:2011:y:2011:i:1:n:326386
    DOI: 10.1155/2011/326386
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    1. Jin, Yongdong & Xu, Jiuping & Zhang, Wenhua & Luo, Jiuli & Xu, Qiwang, 2005. "Simulation of biological waves in single-species bacillus system governed by birth and death-diffusion dynamical equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 68(4), pages 317-327.
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