Initial-boundary value problem for a fractional type degenerate heat equation

Por Wladimir Neves (Instituto de Matemática, Universidade Federal do Rio de Janeiro, Brasil).

Abstract: In this talk, we consider a fractional type degenerate heat equation posed in bounded domains. We show the existence of solutions for measurable and bounded non-negative initial data, and homogeneous Dirichlet boundary condition. The nonlocal diffusion effect relies on an inverse of the s-fractional Laplacian operator, and the solvability is proved for any s , 0 < s < 1.

Periodic perturbations with rotational symmetry of planar systems driven by a central force

Por Alessandro Fonda (Università degli Studi di Udine).

Abstract: We consider periodic perturbations of a central force field having a rotational symmetry, and prove the existence of nearly circular periodic orbits. We thus generalize, in the planar case, some previous bifurcation results obtained by Ambrosetti and Coti Zelati. Our results apply, in particular, to the classical Kepler problem.

On the Cauchy problem for the wave equation on time-dependent domains

Por Rodica Toader (Università degli Studi di Udine).

Abstract: The mathematical formulation of problems in dynamic fracture mechanics leads naturally to the study of the wave equation on domains which vary in time. We provide a notion of solution to the wave equation on a suitable class of time-dependent domains and show existence and uniqueness for the solutions of the Cauchy problem.

The results are obtained in collaboration with G. Dal Maso (SISSA, Trieste).