Coupled diffusion systems with localized nonlinear reactions

M. Pedersen, Zhigui Lin

Research output: Contribution to journalJournal articleResearchpeer-review

Abstract

This paper deals with the blowup rate and profile near the blowup time for the system of diffusion equations uit - δui = ui+1Pi(x0, t), (i = 1,...,k, uk+1 := uu) in Ω × (0, T) with boundary conditions ui = 0 on ∂Ω × [0, T). We show that the solution has a global blowup. The exact rate of the blowup is obtained, and we also derive the estimate of the boundary layer and on the asymptotic behavior of the solution in the boundary layer.
Original languageEnglish
JournalComputers & Mathematics with Applications
Volume42
Issue number6-7
Pages (from-to)807-816
Number of pages10
ISSN0898-1221
DOIs
Publication statusPublished - 2001

Keywords

  • Modeling and Simulation
  • Computational Theory and Mathematics
  • Computational Mathematics
  • Blowup behavior
  • Boundary layer
  • Diffusion equations
  • Localized source
  • Asymptotic stability
  • Boundary conditions
  • Global optimization
  • Mathematical models
  • Parameter estimation
  • Problem solving
  • Coupled diffusion systems
  • Global blowup
  • Localized nonlinear reactions
  • Nonlinear equations

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