Brandle Cerqueira, CristinaChasseigne, E.Ferreira, Raúl2016-01-202016-01-202011-111534-0392https://hdl.handle.net/10016/22186We consider the Cauchy problem posed in the whole space for the following nonlocal heat equation: where is a symmetric continuous probability density. Depending on the tail of , we give a rather complete picture of the problem in optimal classes of data by: estimating the initial trace of (possibly unbounded) solutions; showing existence and uniqueness results in a suitable class; proving blow-up in finite time in the case of some critical growths; giving explicit unbounded polynomial solutions.24engMatemáticasMatemáticas aplicadasresearch articleMatemáticasopen access166361686Communications on Pure and Applied Analysis10