RT journal article
T1 Well-posedness of time-fractional systems in vector-valued Hölder spaces
A1 Alvarez, Edgardo
A1 Lizama, Carlos
A1 Murillo Arcila, Marina
A2 Matemáticas
K1 Well-posedness
K1 block operator matrix
K1 systems of nonlocal partial differential equations
K1 vector-valued H¨older spaces
K1 tempered fractional derivatives
AB We fully characterize the well-posedness in vector-valued Hölder in time spaces of a nonlocalequation involving a closed operatormatrixAwith diagonal domain, defined on a product of Banach spaces,solely in terms of the norm boundedness of a block-operator-valued symbol. We also give vector-valueda priori maximal Hölder inequalities. Our result also contains a characterization in the case of a singleclosed linear operator (not necessarily bounded), which is also new. We show that the condition that A isthe generator of an analytic semigroup is sufficient for the well-posedness. In particular, we show that thewell-posedness holds if the operators on the diagonal of A are generators of analytic semigroups and if theoff-diagonal entries satisfy a smallness condition. We exemplify our main results with abstract as well asconcrete models arising in fluid dynamics.
PB Springer Nature
SN 1424-3199
YR 2026
FD 2026-03
LK http://hdl.handle.net/10498/38911
UL http://hdl.handle.net/10498/38911
LA eng
DS Repositorio Institucional de la Universidad de Cádiz
RD 21-sep-2026