Nonlinear partial differential equations and their applications to
several problems of real world and social sciences.
Non local second gradient Green-Naghdi type thermo-elastic and viscoelastic theories, within the virtual powers format.
Thermodynamics of non local continuum mechanics materials: the winning strategy of the virtual powers method VS the extra fluxes arguments within, by way of examples, third/higher gradient infinitesimal elasticity and thermo-elasticity.
Jeans like instability in novel hyperbolic hydrodinamic models for chemotactic processes in viascoelastic blood flows.
Porous media and air pollution models, within the Cahn-hilliard theory, combined with revised Green-Naghdi heat theories.
Thermal convection problems in Brinkman-Forchheimer porous media: linear and non-linear stability analysis; structural stability.
Continuous dependence on data and uniqueness in direct and inverse
problems.
Hyperbolic systems, properties of wave propagation and theorems on
global existence.
Non isothermal viscoelastic models of Johnson-Segalman type and their applicability in chemotactic phenomena in blood flows, like the growth of tumors.
Relaxation models for Astrophysical settings, within the gravitational instability problem/stellar formation and magnetic reconnection mechanisms, by applying Cattaneo-Christov type hyperbolic heat theories.
Complex/Dyadic type gradient-flux models of Cahn-Hilliard, in viscoelastic settings, in the presence of Green-Naghdi type thermal effects, for water pollution problems in channels.
Non Fourier rigid heat conduction: a revisited Green-Naghdi
theory vs double and triple Tzou phase lag
theories.
