RT Journal Article
T1 Nonlocal heat equations: Regularizing effect, decay estimates and Nash inequalities
A1 Brandle Cerqueira, Cristina
A1 Pablo Martínez, Arturo de
AB 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<p<∞ when the time is large. These properties turn out to depend only on the behaviour of the kernel at the origin or at infinity, respectively, without need of any information at the other end. An equivalence between the decay and a restricted Nash inequality is shown. Finally we deal with the decay of nonlinear nonlocal equations of porous medium type ∂tu+LΦ(u)=0.
PB American Institute of Mathematical Sciences (AIMS)
SN 1534-0392
YR 2018
FD 2018-05
LK https://hdl.handle.net/10016/33755
UL https://hdl.handle.net/10016/33755
LA eng
NO Work partially supported by Spanish project MTM2011-25287.
DS e-Archivo
RD 1 sept. 2024