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Abstract
In this paper, we consider parabolic nonlocal problems in thin domains. Fix and consider
be the solution to
with initial condition
and a kernel of the form
with J non-singular. This corresponds (via a simple change of variables) to the usual nonlocal evolution problem
, in the thin domain
. Our main result says that there is a limit as
of the solutions to our problem and that this limit, when we take its mean value in the
-direction, is a solution to a limit nonlocal problem in the projected set
.
Disclosure statement
No potential conflict of interest was reported by the authors.
Additional information
Funding
The first author (MCP) is partially supported by CNPq [grant number 302960/2014-7]; FAPESP [grant number 2015/17702-3] (Brazil) and the second author (JDR) by MINCYT [grant number MTM2016-68210] (Spain).