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Abstract:
This special session aims to bring together experts in the research area of nonlocal equations, in order to stimulate fruitful discussions concerning the following primary topics:
1) advances in nonlinear diffusion involving nonlocal operators: regularity problems, long time asymptotic behaviour and entropy methods, existence or no existence of free boundaries, discussion of models involving general non-local operators;
2) nonlocal aggregations: state of art concerning many open problems such as typical profiles of blow-up, qualitative properties of the minimizers or steady states and conditions for their existence;
3) balance between nonlinear diffusions and nonlocal attraction for Keller-Segel type related models: new perspectives in the study of a general class of equations in which repulsion is modelled by nonlinear diffusion (fractional or porous medium like) and attraction by nonlocal operators.
4) elliptic theory with nonlocal operators and connections with geometric and probabilistic approaches;
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