Mathematical Analysis Seminar, Academic Year 2024-2025
- Invited Speaker: TRAN BAO NGOC (Institute of Mathematics and Scientific Computing, University of Graz, Austria)
- Date & Time: 22nd of November, 2024, 10:00 - 12:00
- Title: Singular limits arising from biological systems with fast processes and commonly mathematical consideration
- Room: E202B, Nguyen Van Cu Campus.
- Abstract: Many natural processes that happen fast in biological systems have been modelled and studied via mathematical tools. These processes are described by singular terms in systems of ordinary/partial differential equations (ODEs/PDEs) and usually relate to a sufficiently small parameter 0 < ε ≪ 1 (or a sufficiently large parameter λ ∼ 1/ε). This talk discusses such phenomena: “fast switching between healthy roots and toxic roots in plant growth dynamics” and “fast diffusion of chemicals secreted by a species that attract or repulse other species”, where the limits as ε ! 0 are respectively called fast reaction limits [2] and fast signal diffusion limits [3]. Mathematical considerations of these types of limits commonly contain rigorous simplifications of complicated systems of ODEs/PDEs to simpler systems in applications, and convergence rates or the accuracy of the simplified systems, which will be introduced. An interesting case of enzyme kinetics in which the Michaelis-Menten kinetics [1] are no longer applicable, as well as some widely applied models in bio-medicine, will be also linked.
[1] Bao Quoc Tang and Bao-Ngoc Tran. Rigorous derivation of Michaelis-Menten kinetics in the presence of diffusion, to appear in SIAM Journal of Mathematical Analysis, 2024.
[2] Jeff Morgan, Cinzia Soresina, Tang Quoc Bao, and Bao-Ngoc Tran. Plant growth involves toxicity, diffusion, and fast switching, in preparation.
[3] Cordula Reisch, Bao-Ngoc Tran, and Juan Yang. Global existence, fast signal diffusion limit, and L ∞-in-time convergence rates in a competitive chemotaxis system, arXiv:2405.17392, 2024.
- Organizer: LE TRONG THANH, BUI (Vietnam National University – Ho Chi Minh City, University of Science)