DIFFERENTIAL GEOMETRY, CONTINUUM MECHANICS AND MATHEMATICAL PHYSICS Seminar

 

PROGRAM

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Predavanja možete pratiti i online putem MITEAM stranice seminara Diferencijalna geometrija, mehanika kontinuuma i matematička fizika: https://miteam.mi.sanu.ac.rs/asset/YNvstaSeP9v2tgqTP

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Plan rada seminara Diferencijalna geometrija, mehanika kontinuuma i matematička fizika za MAJ 2026.

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Petak, 29.05.2026. u 12:15, Pariske Komune bb, Niš i Live stream
Dušan Zorica, Departman za fiziku, Prirodno-matematički fakultet, Univerzitet u Novom Sadu
ENERGIJA I DISIPIRANA SNAGA ZA JEDNODIMENZIONO VISKOELASTIČNO TELO
Snaga po jedinici zapremine za jednodimenziono viskoelastično telo, opisano konstitutivnim modelom koji sadrži frakcione integrale i Riman-Liuvuilove frakcione izvode, zapisana je u vremenskom domenu, korišćenjem funkcija puzanja i relaksacije, preko člana koji odgovara energiji tela i člana koji opisuje disipiranu snagu. Pokazuje se da je pozitivnost energije i snage disipacije implicirana termodinamičkim restrikcijama na parametre frakcionih Cenerovih i anti-Cenerovih modela, dobijenim razmatranjima u ustaljenom stanju, na koje su nametnuta dodatna ograničenja koja garantuju da su funkcije puzanja i relaksacije redom Bernštajnova i kompletno monotona funkcija. Pretpostavljajući deformaciju u odliku sinusne funkcije, numerički je ispitana vremenska evolucija snage po jedinici zapremine, izražene kako preko funkcije puzanja, tako i preko funkcije relaksacije. Takođe je numerički ispitano da li se grafici zavisnosti energije tela i snage disipacije od vremena poklapaju ukoliko se one izraze preko fukcije puzanja, odnosno funkcije relaksacije.

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Ljubica Oparnica, Faculty of Education in Sombor, University of Novi Sad
THE FRACTIONAL ZENER WAVE EQUATIONS
To model wave propagation in homogeneous viscoelastic media one uses three basic continuum-mechanics equations: the equation of motion, a constitutive law (stress-strain relation), and the symmetric displacement gradient (strain). This system reduces to wave type di erential equations, and using Zeners constitutive law- the simplest model predicting creep recovery and stress relaxation- leads to fractional Zener wave equation. In one dimension works S. Konjik, Lj. Oparnica, D. Zorica, Waves in fractional Zener type viscoelastic media, Journal of Mathematical Analysis and Applications, 365(1) (2010), 259-268, D. Zorica, Lj. Oparnica, Energy dissipation for hereditary and energy conservation for non-local fractional wave equations, Philos. Trans. R. Soc. A 378 (2020), 20190295, and G. Hormann, Lj. Oparnica, D. Zorica, Microlocal analysis of fractional wave equations, Z. Angew. Math. Mech. 97 (2017), 217225 establish existence and uniqueness of solutions to the fractional Zener wave equation in the space of tempered distributions, characterize energy dissipation, and begin microlocal analysis (non-characteristic regularity). Further study, F. Broucke, Lj. Oparnica, Micro-local and qualitative analysis of the fractional Zener wave equation, Journal of Differential Equations 321 (2022), 217-257 complete the description of the C wave-front set showing that unlike the classical wave equation, the fundamental solution here is smooth on the boundary of the forward light cone. Gevrey-class analysis reveals singularities near that boundary for classes close to order 1. Qualitative analysis describes the limiting shape of wave packets and motivates the notion of wave-packet speed. For the 3D bounded Lipschitz domain case, with L variable parameters and density bounded below, well-posedness is proved in Lj. Oparnica, E. Suli, Well-posedness of the fractional Zener wave equation for heterogeneous viscoelastic materials Fractional Calculus and Applied Analysis, 23(1) (2020), 126-166., while S. Gordic, Lj. Oparnica, D. Zorica, The Fractional Zener Wave Equations, submitted to: Journal of Mathematical Analysis and Applications (2026), treats the unbounded 3D domain, derives the fundamental solution for the Cauchy problem, proves an a priori energy dissipation estimate, and presents numerical examples illustrating characteristic fractional e ects. This talk will review these results and present the most interesting parts in detail

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