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Fractional decay bounds for nonlocal zero order heat equations
Author(s) -
Chasseigne E.,
Felmer P.,
Rossi J. D.,
Topp E.
Publication year - 2014
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms/bdu042
Subject(s) - mathematics , bounded function , order (exchange) , zero (linguistics) , combinatorics , polynomial , upper and lower bounds , heat equation , mathematical physics , mathematical analysis , linguistics , philosophy , finance , economics
In this paper, we obtain bounds for the decay rate for solutions to the nonlocal problem∂ t u ( t , x ) = ∫ R n J ( x , y ) [ u ( t , y ) − u ( t , x ) ]d y . Here we deal with bounded kernels J but with polynomial tails, that is, we assume a lower bound of the form J ( x , y ) ⩾ c 1| x − y | − ( n + 2 σ ), for| x − y | > c 2 . Our estimates takes the form∥ u ( t ) ∥L q ( R n )⩽ C t − ( n / 2 σ ) ( 1 − 1 / q )for t large.
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