Perturbation of semi-linear evolution equations under weak assumptions at initial time

Daniel Daners
Preprint, January 2004
Journal of Differential Equations, 210 (2005), 352-382.
Original available at doi:10.1016/j.jde.2004.08.004
Citations on Google Scholar


We prove perturbation results for abstract semi-linear evolution equations in a Banach space. The main feature is that only very weak assumptions are needed at initial time. This allows to prove weak continuity properties and to deal with rather general domain perturbation problems for semi-linear parabolic and hyperbolic boundary value problems with various boundary conditions. The theory also implies the well known theory on parameter dependent equations.

AMS Subject Classification (2000): 34G20 (34D20 35K60)

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