Isothermalisation for a non-local heat equation

Emmanuel Chasseigne ^[2] ; Raul Ferreira ^[1]
1. [1] Universidad Complutense de Madrid
  
  Universidad Complutense de Madrid
  
  Madrid, España
2. [2] Universite de Tours, France
Localización: Annali della Scuola Normale Superiore di Pisa. Classe di scienze, ISSN 0391-173X, Vol. 13, Nº 4, 2014, págs. 1115-1132
Idioma: inglés
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Resumen
- In this paper we study the asymptotic behavior for a nonlocal heat equation in an inhomogenous medium:
  
  ⇢(x)ut = J ⇤ u − u in RN ⇥ (0,1) , where ⇢ is a continuous positive function, u is non-negative and J is a probability measure having finite second-order momentum. Depending on integrability conditions on the initial data u0 and ⇢, we prove various isothermalisation results, i.e., u(t) converges to a constant state in the whole space.