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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.
MSC:
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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