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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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