Well-posedness of quasilinear parabolic equations in time-weighted spaces

Well-posedness in time-weighted spaces of certain quasilinear (and semilinear)parabolic evolution equationsu '=A(u)u+f(u) is established. The focus lies on thecase of strict inclusions dom(f) subset of(dom(A) of the domains of the nonlinearitiesu -> f(u) andu -> A(u). Based on regularizing effects of parabolic equations it isshown that a semiflow is generated in intermediate spaces. In applications this allowsone to derive global existence from weaker a priori estimates. The result is illustratedby examples of chemotaxis systems.