Unbounded solutions of the nonlocal heat equation

Cristina Brändle (1) , Emmanuel Chasseigne (2, 3) , Raul Ferreira (4)

1 Departamento de Matematicas
2 FDP - Fédération de recherche Denis Poisson
3 LMPT - Laboratoire de Mathématiques et Physique Théorique
4 Departamento de Matematica Aplicada [Madrid]

We consider the Cauchy problem posed in the whole space for the following nonlocal heat equation: u_t = J ∗ u − u , where J is a symmetric continuous probability density. Depending on the tail of J, we give a rather complete picture of the problem in optimal classes of data by: (i) estimating the initial trace of (possibly unbounded) solutions; (ii) showing existence and uniqueness results in a suitable class; (iii) giving explicit unbounded polynomial solutions.

Mots clés: Non-local diffusion; initial trace; optimal classes of data.

Mots clés: optimal classes of data

Domaines: Equations aux dérivées partielles [math.AP]

Cristina Brändle, Emmanuel Chasseigne, Raul Ferreira. Unbounded solutions of the nonlocal heat equation. Communications on Pure and Applied Analysis, 2011, 10, pp.1663-1686. ⟨hal-00447374v2⟩