M0998 Reading seminar: Reaction-Diffusion Systems

Faculty of Science
Spring 2024
Extent and Intensity
0/1/0. 2 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: z (credit).
Teacher(s)
doc. Phuoc Tai Nguyen, PhD (lecturer)
Guaranteed by
doc. Phuoc Tai Nguyen, PhD
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Mon 19. 2. to Sun 26. 5. Wed 16:00–16:50 MS1,01016
Prerequisites
Calculus of multiple variables, Linear Algebra, Functional analysis, Ordinary differential equations, Partial differential equations.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The reading seminar aims to establish a forum for students to explore and delve into the theory of reaction-diffusion systems and related systems stemming from chemistry and biology. This will be implemented through discussions and seminar presentations.
Learning outcomes
By the end of the reading seminar, students should have acquired knowledge of recent developments, mastery of various methods and techniques, and the ability to effectively present research papers in the theory of reaction-diffusion systems. These competencies are important for pursuing independent research in this feld.
Syllabus
  • Motivations and derivations of some reaction-diffusion systems (RDSs),
  • Local existence and a priori estimates,
  • Duality and improved duality methods,
  • Global existence of bounded solutions,
  • Construction of blow-up solutions,
  • Recent extension to RDSs with a nonlocal diffusion,
  • Cross-diffusion systems.
Literature
  • DAOUD, Maha, Laamri EL-HAJ and Azeddine BAALAL. A class of fractional parabolic reaction-diffusion systems with control of total mass: theory and numerics. arXiv preprint arXiv:2306.03836. 2023. info
  • MICHEL, Pierre and Didier SCHMITT. Examples of finite time blow up in mass dissipative reaction-diffusion systems with superquadratic growth. Discrete and Continuous Dynamical Systems. Springfield, Missouri: AIMS (American Institute of Mathematical Sciences), 2023, vol. 43, 3,4, p. 1686-1701. ISSN 1078-0947. info
  • JÜNGEL, Ansgar and Nicola ZAMPONI. Analysis of a fractional cross-diffusion system for multi-species populations. Electronic Journal of Differential Equations. 2022, vol. 322, p. 237-267. ISSN 1072-6691. info
  • KOSTIANKO, Anna, Chunyou SUN and Sergey ZELIK. Reaction-diffusion systems with supercritical nonlinearities revisited. Mathematische annalen. Berlin: Verlag von Julius Springer, 2022, vol. 384, 1-2, p. 1-45. ISSN 1432-1807. info
  • FELLNER, Klemens, Jeff MORGAN and Bao Quoc TANG. Global classical solutions to quadratic systems with mass control in arbitrary dimensions. 2020. info
  • PIERRE, Michel. Global existence in reaction-diffusion systems with control of mass: a survey. MILAN JOURNAL OF MATHEMATICS. SWITZERLAND: SPRINGER BASEL AG, 2010, vol. 78, p. 417-455. ISSN 1424-9286. info
Teaching methods
Students' reports and presentation with a discussion.
Assessment methods
Evaluation of an activity.
Language of instruction
English
Further Comments
The course is taught only once.
  • Enrolment Statistics (recent)
  • Permalink: https://is.muni.cz/course/sci/spring2024/M0998