Fisica Matematica

The main research topics of the Group include: mathematical modeling of complex systems, dynamical systems and solvable models, properties and applications of special functions, controllability of solutions and analysis of contact and transmission problems, materials with memory (thermo-viscoelastic solids and fluids, hereditary heat conductors, ...), phase transition phenomena. In particular, the members of the group have specific knowledge on: 1) Phase transition phenomena, modeling and investigations on direct and control problems (e.g. non isochoric phase separation induced both by temperature and pressure, non isothermal, anisotropic, phase-field models describing spontaneous magnetization, non isothermal phase-field models describing isotropic-nematic transition in liquid crystals, dynamics in ferromagnets and ferroelectrics, well-posedness results and longtime behaviour of solutions for singular phase-field models, global longtime behavior in phase-field non-linear models with thermal memory (Coleman-Gurtin heat flux law), stability of solutions to nonlinear thermodynamic systems involving singular potentials, boundary controllability of solutions to phase-field models describing first order transition). 2) Viscoelastic materials: modeling and investigations on direct problems (e.g. studies on thermo-viscoelatic beams or plates involving a nonlinear term accounting for their extensibility (Woinovsky-Krieger, Berger, etc.) with different constitutive laws for the heat flux (Fourier, Coleman-Gurtin, Gurtin-Pipkin), researches on suspension bridge equations, viscoelastic models with nonlinear memory, analysis of the aging in viscoelasticity, steady-states analysis of nonlinear problems in coupled structures, longtime behavior and existence of the global attractor for the thermo-viscoelastic extensible beam, control on the boundary for transmission problems in composite (elastic and thermo-viscoelatic) materials, determination of constitutive parameters in a (elastic/viscoelastic/thermo-viscoelastic) multilayer through data associated with the reflected wave in a reflection-transmission process. 3) Bäcklund transformations: constructions of Bäcklund transformations for ODES and PDEs and their applications (e.g. to problems of physical interests modeled by the Emden Fowler equation, the Ermakov Pinney equation and the Gross-Pitaevskii equation and its reductions). 4) Study of equilibrium and non-equilibrium processes in heat and mass transfer: modeling and applications (e.g. extension and quantification of entropy, energy and mechanical work to non-equilibrium phenomena, optimization of thermal rectification devices, optimization of convecting-radiating longitudinal fins). 5) Study of the properties of solutions of ODEs in the complex domain: distribution of ploes and zeros, series expansions, connection formulae, applications (e.g. investigations on the properties of the solutions of the Airy equation, of the non-homogeneous Airy equation, and of the Painlevé equations I, II and IV).