[Turkmath:6564] The Announce of Weekly Online Seminar “Analysis and Applied Mathematics"

[Allaberen Ashyralyev]

Dear All,
You are cordially invited to the  Weekly Online Seminar “Analysis and
Applied Mathematics” on
*Date*: Tuesday, June 25, 2024
*Time:* 14.00-15.00 (Istanbul) = 13.00-14.00 (Ghent) = 16.00-17.00 (Almaty)
*Place:* Zoom link:
https://us02web.zoom.us/j/6678270445?pwd=SFNmQUIvT0tRaHlDaVYrN3l5bzJVQT09,
Conference ID: 667 827 0445, Access code: 1
*Speaker: *Dr. Gülsemay Yiğit

Bahçeşehir University, Istanbul, Türkiye

*Title:*  Rigorous mathematical analysis and simulations of
reaction-diffusion systems with linear cross-diffusion on convex and
non-convex domains
*Abstract:* In this talk, a domain-dependent mathematical analysis of
reaction-diffusion systems is presented to understand the role of geometry
and cross-diffusion in pattern formation. Linear stability analysis is
employed to derive the constraints which are necessary in understanding the
dual roles of linear cross-diffusion and domain-size for studying
the instability of a reaction-diffusion system. Theorems are stated for the
conditions for Turing, Hopf and transcritical instabilities are proven in
terms of lower and upper bounds of the domain-size together with the
reaction, self- and cross-diffusion coefficients. These bounds allow for
the full parameter classification of the model system, which is presented
in terms of the relationship between the domain size, self and
cross-diffusion parameters. Regions showing Turing instability, Hopf and
transcritical types of bifurcations are demonstrated using the parameter
values of the system. To support theoretical findings, a state-of-the-art
finite element method is employed. The finite element method is a numerical
method that solves highly nonlinear systems of partial differential
equations on complex geometries. The finite element numerical solutions
reveal spatial and spatiotemporal patterns on rectangular, circular, and
annular geometries, with no flux boundary conditions. Observed patterns on
non-convex geometries, for example, resemble ring-shaped
cross-sectional scans of hypoxic tumours. Specifically, the cross-section
of an actively invasive region in a hypoxic tumour can be effectively
approximated by an annulus.
 *Abstracts and forthcoming talks can be found on our webpage*
https://sites.google.com/view/aam-seminars
With my best wishes
*Prof. Dr. Allaberen Ashyralyev *
*Department of Mathematics, Bahcesehir University,**34349**, Istanbul,
Turkiye*
*Peoples' Friendship University of Russia (RUDN University),** Ul Miklukho
Maklaya 6, Moscow 117198, Russian Federation *
*Institute of Mathematics and Mathematical Modelling, 050010, Almaty,
Kazakhstan*
*e-mail: allaberen.ashyralyev at bau.edu.tr
<allaberen.ashyralyev at neu.edu.tr> and **aallaberen at gmail.com
<aallaberen at gmail.com> *
 http://akademik.bahcesehir.edu.tr/web/allaberenashyralyev

https://sites.google.com/view/aam-seminars

https://ejaam.org/editorial.html

*https://icaam-online.org/ <https://icaam-online.org/>*

*https://www.genealogy.math.ndsu.nodak.edu/id.php?id=95872&fChrono=1
<https://www.genealogy.math.ndsu.nodak.edu/id.php?id=95872&fChrono=1>*
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