Nonlocal heat equations: Regularizing effect, decay estimates and Nash inequalities Articles uri icon

publication date

  • May 2018

start page

  • 1161

end page

  • 1178

issue

  • 3

volume

  • 17

International Standard Serial Number (ISSN)

  • 1534-0392

Electronic International Standard Serial Number (EISSN)

  • 1553-5258

abstract

  • We study the short and large time behaviour of solutions of nonlocal heat equations of the form ∂tu+Lu=0. Here L is an integral operator given by a symmetric nonnegative kernel of Lévy type, that includes bounded and unbounded transition probability densities. We characterize when a regularizing effect occurs for small times and obtain Lq-Lp decay estimates, 1≤q

keywords

  • nonlocal diffusion equations; integral operators; asymptotic behaviour; nash inequalities