Resumen de Isothermalisation for a non-local heat equation

Emmanuel Chasseigne, Raul Ferreira de Pablo

• 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.