Analysis of evolutive partial differential equations
Strani Marta, University Researchers with fixed-term contract (Italian Law 240/10)
C. Mascia, Sapienza, Università di Roma
M. Garrione, Politecnico di Milano
R. Folino, Università dell’Aquila
G. Palatucci, Università di Parma
B. Texier, Universitè Paris Diderot, Parigi
M. Goldman, Universitè Paris Diderot, Parigi
L. De Luca, SISSA, Trieste
F. Petitta, F. Oliva, Sapienza, Università di Roma
Stability and metastability for reaction-convection-diffusion equations with nonlinear diffusions
The study of the asymptotic behavior of the solutions to some one dimensional evolutive PDEs with nonlinear diffusion, to be considered in bounded intervals. Particular attention is devoted to mean curvature type diffusions, which find application, for example, in biophysics, chemical physics, population genetics and mathematical ecology.
The influence of viscosity in the instabilities of some hydrodynamical equations
The study the phenomenon of time-delayed instabilities for hyperbolic partial differential equations, among which equations that emerge in the study of fluid dynamics (for example, the Euler equations with viscosity).
Multiscale phenomena in gradient flow equations
The study partial differential equations of gradient flow type, with particular attention to equations that emerge in mathematical physics and describe the phenomenon of phase transitions (Allen-Cahn and Cahn-Hilliard equations). the study of multiscale phenomena (fast-slow dynamics) through the study of the energy associated to the system.
Well posedness for singular elliptic systems
The study of semilinear elliptic problems with lower-order terms depending on the solution and that are singular in the region where this solution vanishes. The singularities will be given by singular terms, irregular data and general nonlinearities.
Last update: 15/09/2020