Naslov
Dynamics of Extended Gradient Systems

Autori
Slijepčević, Siniša

Vrsta, podvrsta i kategorija rada
Sažeci sa skupova, sažetak, znanstveni

Izvornik
Dynamics of Extended Gradient Systems / Turaev, Dimitry ; Zelig, Sergey - Nižni Novgorod, 2015, 18-18

Skup
Conference on Infinite Dimensional Dynamical Systems

Mjesto i datum
Nižni Novgorod, Ruska Federacija, 13.07.2015. - 17.07.2015

Vrsta sudjelovanja
Pozvano predavanje

Vrsta recenzije
Međunarodna recenzija

Ključne riječi
Attractors ; Energy inequalities ; Partial Differential Equations

Sažetak
Extended gradient systems are dynamical systems on unbounded domains, which when suitably restricted to a finite domain are gradient-like. We present general results on the structure of ω -limit sets, invariant measures, and stability of equilibria and invari- ant manifolds. We then apply the results to a series of examples, illustrating similarities and differences with gradient-like systems. The general theory yields some new results in the following examples on unbounded domains: dynamics of various reaction-diffusion equations (with energy, entropy, and Zelenyak/Matano/Fiedler/Rocha-like Lyapunov functions) ; dynamics of unforced Navier- Stokes equation in 2D ; construction of orbits and measures of Lagrangian systems and related formally gradient dynamics of the action functional ; and finally asymptotics of some Markov chains on infinite lattices and related phase transitions. For such systems we also often obtain new bounds on relaxation times on bounded domains, independent of the domain size.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA