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Galerkin approximations for nonlinear evolution inclusions. (English) Zbl 0819.34011
The paper deals with the convergence properties of the Galerkin approximations to a nonlinear nonautonomous evolution inclusion. In particular it is shown that the solution set is compact and connected in the Lebesgue-Bochner space \(L^ p ([0,b], H)\), where \(H\) is a separable Hilbert space. Moreover, the existence of periodic solutions is proven. The applicability of these results is illustrated in an example of multivalued parabolic partial differential equations.
34A60 Ordinary differential inclusions
34G20 Nonlinear differential equations in abstract spaces
35B10 Periodic solutions to PDEs
35G10 Initial value problems for linear higher-order PDEs
35K25 Higher-order parabolic equations
34G99 Differential equations in abstract spaces
35R70 PDEs with multivalued right-hand sides
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