Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
842318 | Nonlinear Analysis: Theory, Methods & Applications | 2008 | 30 Pages |
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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Authors
Toshitaka Matsumoto, Naoki Tanaka,