We have located links that may give you full text access.
Early and late stage profiles for a chemotaxis model with density-dependent jump probability.
Mathematical Biosciences and Engineering : MBE 2018 December 2
In this paper, we derive a chemotaxis model with degenerate diffusion and density-dependent chemotactic sensitivity, and we provide a more realistic description of cell migration process for its early and late stages. Different from the existing studies focusing on the case of non-degenerate diffusion, this model with degenerate diffusion causes us some essential difficulty on the boundedness estimates and the propagation behavior of its compact support. In the presence of logistic damping, for the early stage before tumour cells spread to the whole domain, we first estimate the expanding speed of tumour region as O(t^β) for 0 < β < 1/2 . Then, for the late stage of cell migration, we further prove that the asymptotic profile of the original system is just its corresponding steady state. The global convergence of the original weak solution to the steady state with exponential rate O(e^(-ct)) for some c < 0 is also obtained.
Full text links
Related Resources
Trending Papers
Challenges in Septic Shock: From New Hemodynamics to Blood Purification Therapies.Journal of Personalized Medicine 2024 Februrary 4
Molecular Targets of Novel Therapeutics for Diabetic Kidney Disease: A New Era of Nephroprotection.International Journal of Molecular Sciences 2024 April 4
The 'Ten Commandments' for the 2023 European Society of Cardiology guidelines for the management of endocarditis.European Heart Journal 2024 April 18
A Guide to the Use of Vasopressors and Inotropes for Patients in Shock.Journal of Intensive Care Medicine 2024 April 14
Diagnosis and Management of Cardiac Sarcoidosis: A Scientific Statement From the American Heart Association.Circulation 2024 April 19
Essential thrombocythaemia: A contemporary approach with new drugs on the horizon.British Journal of Haematology 2024 April 9
Get seemless 1-tap access through your institution/university
For the best experience, use the Read mobile app
All material on this website is protected by copyright, Copyright © 1994-2024 by WebMD LLC.
This website also contains material copyrighted by 3rd parties.
By using this service, you agree to our terms of use and privacy policy.
Your Privacy Choices
You can now claim free CME credits for this literature searchClaim now
Get seemless 1-tap access through your institution/university
For the best experience, use the Read mobile app