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Non-equilibrium Thermodynamics of Hyperbolic Systems
Sýkora, Martin ; Pavelka, Michal (advisor) ; Hütter, Markus (referee) ; Lukáčová - Medvidová, Mária (referee)
Continuum mechanics and thermodynamics have been used in many fields from sci- ence to industry to medicine. While simple materials have already been described, for instance by the famous Navier-Stokes equations, more complex materials like superfluids are still not completely understood. Multiple frameworks, often based on balance laws and thermodynamic closures, are used. In this thesis, an alternative General Equation for Non-Equilibrium Reversible-Irreversible Coupling (GENERIC) framework is studied. We apply this method, based on Hamiltonian mechanics and gradient dynamics, to a wide range of settings from a simple continuum to mixtures, superfluids and non-Fourier heat conduction. We study the symmetric hyperbolicity of the resulting equations, as it guarantees the well-posedness of the system, and suggest extensions to the already-known symmetric hyperbolic equations. We derive new models, compare them to more classical theories and study what phenomena they can and cannot describe, both analytically and numerically. 1
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