TY - UNPB

T1 - Well-Posedness of Quasilinear Parabolic Equations in Time-Weighted Spaces

AU - Matioc, Bogdan

AU - Walker, Christoph

N1 - 26 pages; includes revised examples

PY - 2023/12/13

Y1 - 2023/12/13

N2 - Well-posedness in time-weighted spaces of certain quasilinear (and semilinear) parabolic evolution equations \(u'=A(u)u+f(u)\) is established. The focus lies on the case of strict inclusions \(\mathrm{dom}(f)\subsetneq \mathrm{dom}(A)\) of the domains of the nonlinearities \(u\mapsto f(u)\) and \(u\mapsto A(u)\). Based on regularizing effects of parabolic equations it is shown that a semiflow is generated in intermediate spaces. In applications this allows one to derive global existence from weaker a priori estimates. The result is illustrated by examples of chemotaxis systems.

AB - Well-posedness in time-weighted spaces of certain quasilinear (and semilinear) parabolic evolution equations \(u'=A(u)u+f(u)\) is established. The focus lies on the case of strict inclusions \(\mathrm{dom}(f)\subsetneq \mathrm{dom}(A)\) of the domains of the nonlinearities \(u\mapsto f(u)\) and \(u\mapsto A(u)\). Based on regularizing effects of parabolic equations it is shown that a semiflow is generated in intermediate spaces. In applications this allows one to derive global existence from weaker a priori estimates. The result is illustrated by examples of chemotaxis systems.

KW - math.AP

U2 - 10.48550/arXiv.2312.07974

DO - 10.48550/arXiv.2312.07974

M3 - Preprint

BT - Well-Posedness of Quasilinear Parabolic Equations in Time-Weighted Spaces

ER -