Global well-posedness and invariant regions for a one-dimensional RD-ARD glioblastoma model
Year: 2026
Type: article
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. For more information and the latex files, see https://ejde.math.txstate.edu/Volumes/2026/68/abstr.html
Authors: Zhipeng Yang, Zhenyu Zhan
Institution: Yunnan Normal University
Language: English
Subfield: Modeling and Simulation
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
Awards: G6285904573, G7357072266, G7592286726
OpenAlex ID: W7213235528