About Myrto Galanopoulou Myrto Galanopoulou Ph.D. Student, Applied Mathematics and Computational Science Analysis of PDE's Conservation Laws Short Bio Dr. Myrto Galanopoulou received a B.Sc. and a M.Sc. in Applied Mathematics in 2015 from the University of Crete and a Ph.D. from KAUST in 2020. During her Ph.D. studies she worked on the problem of polyconvex thermoelasticity. In September 2021 she joined the School of Mathematical And Computer Sciences, Heriot-Watt University, as a Research Associate Fellow. Dr. Galanopoulou's research interests lie in the area of analysis of partial differential equations with applications in fields as continuum physics or mechanics. Currently she is working on the mathematical theory of Events Presented Events Nov 8 - Nov 14, 2020 The equations of polyconvex thermoelasticity Myrto Galanopoulou, Ph.D. Student, Applied Mathematics and Computational Science Nov 9, 17:00 - 19:00 KAUST In my thesis, I consider the system of thermoelasticity endowed with polyconvex energy. After presenting the equations in their mathematical and physical context, I embed the equations of polyconvex thermoviscoelasticity into an augmented, symmetrizable, hyperbolic system which possesses a convex entropy. This allows to prove many important stability results, such as convergence from thermoviscoelasticity (with Newtonian viscosity and Fourier heat conduction) to smooth solutions of the system of adiabatic thermoelasticity, and convergence from thermoviscoelasticity to smooth solutions of thermoelasticity in the zero-viscosity limit. In addition, I establish a weak-strong uniqueness result in the class of entropy weak solutions and in a suitable class of measure-valued solutions, defined by means of generalized Young measures that describe both oscillatory and concentration effects. Also, I construct a variational scheme for isentropic processes of adiabatic polyconvex thermoelasticity: I establish existence of minimizers which converge to a measure-valued solution that dissipates the total energy, while the scheme converges when the limiting solution is smooth.
The equations of polyconvex thermoelasticity Myrto Galanopoulou, Ph.D. Student, Applied Mathematics and Computational Science Nov 9, 17:00 - 19:00 KAUST In my thesis, I consider the system of thermoelasticity endowed with polyconvex energy. After presenting the equations in their mathematical and physical context, I embed the equations of polyconvex thermoviscoelasticity into an augmented, symmetrizable, hyperbolic system which possesses a convex entropy. This allows to prove many important stability results, such as convergence from thermoviscoelasticity (with Newtonian viscosity and Fourier heat conduction) to smooth solutions of the system of adiabatic thermoelasticity, and convergence from thermoviscoelasticity to smooth solutions of thermoelasticity in the zero-viscosity limit. In addition, I establish a weak-strong uniqueness result in the class of entropy weak solutions and in a suitable class of measure-valued solutions, defined by means of generalized Young measures that describe both oscillatory and concentration effects. Also, I construct a variational scheme for isentropic processes of adiabatic polyconvex thermoelasticity: I establish existence of minimizers which converge to a measure-valued solution that dissipates the total energy, while the scheme converges when the limiting solution is smooth.
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