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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.

47H20 Semigroups of nonlinear operators
47H14 Perturbations of nonlinear operators
34G20 Nonlinear differential equations in abstract spaces
35K90 Abstract parabolic equations
Full Text: DOI
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