Department of Mathematics
Yunnan Normal University, Kunming, China
email: yangzhipeng326@163.com
Department of Mathematics
Yunnan Normal University, Kunming, China
email: 20972850@qq.com
Zhipeng Yang, Zhenyu Zhan
Abstract:
We study a one-dimensional reaction-diffusion and advection-reaction-diffusion
system arising from a heterogeneous glioblastoma model with shared crowding effects.
The two components represent latent subpopulation densities that both diffuse and
proliferate; the second is additionally subject to a constant advective bias,
with crowding coupled through the total density. On a bounded interval,
under either componentwise Neumann conditions or the natural zero-flux condition
for the advective component, we establish a global well-posedness theory,
positivity preservation, invariant regions, and uniform absorbing bounds in the
supremum norm. Under the zero-flux condition, the invariant and absorbing upper
barriers for the second component carry the exponential spatial weight \(e^{(a/ D_v)x}\),
in contrast to the constant barriers available under componentwise Neumann conditions.
We further formulate the associated semiflow and prove the existence of a global
attractor.
Submitted June 25 2026. Published September 9, 2026.
Math Subject Classifications: 35K57, 35B40, 92C50.
Key Words: Reaction-diffusion-advection system; glioblastoma model; global well-posedness.
DOI: 10.58997/ejde.2026.68
Show me the PDF file (463 KB), TEX file for this article.
|
Zhipeng Yang Department of Mathematics Yunnan Normal University, Kunming, China email: yangzhipeng326@163.com |
|---|---|
|
Zhenyu Zhan Department of Mathematics Yunnan Normal University, Kunming, China email: 20972850@qq.com |
Return to the EJDE web page