Structured populations with diffusion and Feller conditions

Agnieszka  Bartłomiejczyk; Henryk  Leszczyński; Agnieszka  Bartłomiejczyk; Henryk  Leszczyński

doi:10.3934/mbe.2015002

Mathematical Biosciences and Engineering

2016, Volume 13, Issue 2: 261-279. doi: 10.3934/mbe.2015002

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Structured populations with diffusion and Feller conditions

1.
Faculty of Applied Physics and Mathematics, Gdańsk University of Technology, Gabriela Narutowicza 11/12, 80-233 Gdańsk
2.
Institute of Mathematics, University of Gdańsk, Wita Stwosza 57, 80-952 Gdańsk

Received: 01 February 2015 Accepted: 29 June 2018 Published: 25 November 2015
MSC : Primary: 35Q92, 92D25; Secondary: 47N60, 35B35.

We prove a weak maximum principle for structured population models with dynamic boundary conditions. We establish existence and positivity of solutions of these models and investigate the asymptotic behaviour of solutions. In particular, we analyse so called size profile.
- Size-structured model,
- diffusion,
- Fourier analysis.,
- size profile,
- maximum principle,
- Feller boundary condition
Citation: Agnieszka Bartłomiejczyk, Henryk Leszczyński. Structured populations with diffusion and Feller conditions[J]. Mathematical Biosciences and Engineering, 2016, 13(2): 261-279. doi: 10.3934/mbe.2015002

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Abstract

We prove a weak maximum principle for structured population models with dynamic boundary conditions. We establish existence and positivity of solutions of these models and investigate the asymptotic behaviour of solutions. In particular, we analyse so called size profile.

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