On a Parabolic–Elliptic system with chemotaxis and logistic type growth

We consider a nonlinear PDEs system of two equations of Parabolic–Elliptic type with chemotactic terms. The system models the movement of a biological population “u” towards a higher concentration of a chemical agent “w” in a bounded and regular domain Ω⊂RN for arbitrary N∈N. After normalization, the system is as followsut−Δu=−div(umχ∇w)+μu(1−uα), in ΩT=Ω×(0,T),−Δw+w=uγ, in ΩT, for some positive constants m, χ, μ, α and γ, with positive initial datum u0 and Neumann boundary conditions. We study the range of parameters and constrains for which the solution exists globally in time. If either [formula omitted] the solution exists globally in time. Moreover, if α≥m+γ−1 and μ>2χ, and there exist positive constants u‾0 and u_0 such that 0<u_0≤u0≤u‾0<∞ we have that‖u−1‖L∞(Ω)+‖w−1‖L∞(Ω)→0 as t→∞. © 2016 Elsevier Inc.

Авторы
Galakhov E. 1 , Salieva O.2 , Tello J.I.3, 4
Издательство
Academic Press Inc.
Номер выпуска
8
Язык
Английский
Страницы
4631-4647
Статус
Опубликовано
Том
261
Год
2016
Организации
  • 1 Peoples' Friendship University of Russia, Miklukho-Maklaya str. 6, Moscow, 117198, Russian Federation
  • 2 Moscow State Technological University “Stankin”, Vadkovsky lane 3a, Moscow, 125994, Russian Federation
  • 3 Departamento de Matemática Aplicada, ETSI Sistemas Informáticos, Universidad Politécnica de Madrid, Campus Sur, Madrid, 28031, Spain
  • 4 Center for Computation and Simulation, Universidad Politécnica, de Madrid, Campus de Montegancedo, Boadilla del Monte, Madrid, 28660, Spain
Ключевые слова
Asymptotic behavior; Chemotaxis; Global existence; Parabolic–Elliptic systems; Stability
Дата создания
19.10.2018
Дата изменения
03.03.2021
Постоянная ссылка
https://repository.rudn.ru/ru/records/article/record/3772/
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