Título: Modelling Self-organization or Disorder

Orador: Miroslaw Lachowicz (Faculty of Mathematics, Informatics and Mechanics, University of Warsaw, Poland)

Data: sexta-feira, 12 de Abril de 2024, 11h00min

Local: UMinho, campus de Gualtar, sala de seminários

Grupo: Análise e Aplicações

Resumo: I am going to show, that the blow-ups of solutions, that usually are treated as something "very bad", can in fact describe some self-organization phenomena, "positive" (like healing) or "negative" (like society polarization) - [1, 2]. Mathematically it is the theory of integro-differential equations (kinetic equations) that is applied to processes in Social Sciences (opinion formation) - [6], Economics ("lemons and cherries" theory) - [7], Biology (DNA denaturation) - [4], Medicine (tendon healing process) - [5] and the redistribution in a lift - [3].

[1] M. Lachowicz, H. Leszczynski, M. Parisot (2016). A simple kinetic equation of swarm formation: Blow-up and global existence, Appl. Math. Letters, 57, 104-107.

[2] M. Lachowicz, H. Leszczynski, M. Parisot (2017). Blow-up and global existence for a kinetic equation of swarm formation, Math. Models Methods Appl. Sci., 27, 1153-1175.

[3] M. Dol n, M. Lachowicz, A. Schadschneider (2018). A Microscopic Model of Redistribution of Individuals Inside an "Elevator", Springer Nature 2018, P. Dryga u, S. Rogosin (Eds.), Modern Problems in Applied Analysis, Trends in Mathematics, 2018, 77-86.

[4] M. Debowski, M. Lachowicz, Z. Szymanska (2019). Microscopic description of DNA thermal denaturation, Appl. Math. Computation, 361, 47-60.

[5] G. Dudziuk, M. Lachowicz, H. Leszczynski, Z. Szymanska (2019). A simple model of collagen remodeling, Discrete Contin. Dyn. Syst. Ser. B, 24, 2205-2217.

[6] M. Lachowicz, H. Leszczynski, E. Puzniakowska-Gauch (2019). Diffusive and antidiffusive behavior for kinetic models of opinion dynamics, Symmetry, 11, 1024.

[7] M. Lachowicz, H. Leszczynski (2020). Modeling asymmetric interactions in economy, Mathematics, 8, 523-537.