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Semigroups of locally Lipschitz operators associated with semilinear evolution equations of parabolic type. (English) Zbl 1169.47045
The authors characterize semigroups of locally Lipschitz operators on a Banach space $$X$$, providing mild solutions to the Cauchy problem for the semilinear evolution equation $$u'(t)=(A+B)u(t)$$, where $$A$$ is the infinitesimal generator of an analytic semigroup, and $$B$$ is a locally continuous nonlinear operator defined on some subset of $$X$$. Applications are given to the global solvability of the mixed problem for the complex Ginzburg–Landau equation.

##### MSC:
 47H20 Semigroups of nonlinear operators 47H14 Perturbations of nonlinear operators 34G20 Nonlinear differential equations in abstract spaces 35K90 Abstract parabolic equations
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##### References:
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