Article ID Journal Published Year Pages File Type
842318 Nonlinear Analysis: Theory, Methods & Applications 2008 30 Pages PDF
Abstract

A characterization problem is discussed, of semigroups of locally Lipschitz operators providing mild solutions to the Cauchy problem for the semilinear evolution equation of parabolic type u′(t)=(A+B)u(t)u′(t)=(A+B)u(t) for t>0t>0. By parabolic type we mean that the operator AA is the infinitesimal generator of an analytic (C0)(C0) semigroup on a general Banach space XX. The operator BB is assumed to be locally continuous from a subset of YY into XX, where YY is a Banach space which is contained in XX and has a stronger norm defined through a fractional power of −A−A. The characterization is applied to the global solvability of the mixed problem for the complex Ginzburg–Landau equation.

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