Department of Mathematics
Faculty of Science, Hacettepe University
Beytepe 06800, Ankara, Turkey
email: semasimsek@hacettepe.edu.tr
Sema Yayla
Abstract:
In this article, we analyze the long-time dynamics of a Cahn-Hilliard tumor growth model,
focusing on the geometric structure and stability of its global attractors.
Using a Lojasiewicz-Simon type inequality, we first prove that every full trajectory
in the global attractor converges to a single stationary point as \(t \to \infty\) and
to another stationary point as \(t \to -\infty\). As a result, we show that the global
attractor is the union of the unstable manifolds emanating from the stationary points.
We also examine the rate of convergence to these stationary points and provide specific
polynomial and exponential rates under certain conditions. Additionally, we demonstrate
that the global attractors of the corresponding tumor growth model exhibit
upper-semicontinuity with respect to small perturbations of the chemotaxis parameter.
Finally, by restricting chemotaxis within a certain interval, we establish the
lower-semicontinuity of the global attractors for this model.
Submitted May 7, 2025. Published October 21, 2025.
Math Subject Classifications: 35B40, 35D30, 35K57, 35Q92, 37L30, 92C17.
Key Words: Tumor growth model; Cahn-Hilliard equation; long-time dynamics; global attractor
DOI: 10.58997/ejde.2025.100
Show me the PDF file (427 KB), TEX file for this article.
|
Sema Yayla Department of Mathematics Faculty of Science, Hacettepe University Beytepe 06800, Ankara, Turkey email: semasimsek@hacettepe.edu.tr |
|---|
Return to the EJDE web page