Attractors of multivalued semiflows generated by differential inclusions and their approximations. (English) Zbl 1014.35010

Let \(H\) be a real separable Hilbert space, \(\varphi:H \to(-\infty, +\infty]\) a proper convex lower semicontinuous function and let \(\partial \varphi:D (\partial\varphi) \subset H\to 2^H\) be its subdifferential. The authors consider the following differential inclusion \[ {dy\over dt} \in-\partial \varphi(y)+ F(y),\quad t\in[0,T] \]
\[ y(0)= y_0\in H, \] where \(F:H\to 2^H\) is a multivalued mapping. They study the existence of the global compact attractor of a multivalued semiflow for the above problem, extending the result of V. S. Mel’nik and J. Valero [Dopov. Nats. Akad. Nauk Ukr., Mat. Pryr. Tekh. Nauky 2001, No. 10, 7-12 (2001; Zbl 0983.35152)]. And also, they study the continuity and upper semicontinuity of the attractors for approximating and perturbed inclusions. The result is very nice.


35B41 Attractors
35B40 Asymptotic behavior of solutions to PDEs
35K85 Unilateral problems for linear parabolic equations and variational inequalities with linear parabolic operators
47J35 Nonlinear evolution equations
35R70 PDEs with multivalued right-hand sides
35K90 Abstract parabolic equations


Zbl 0983.35152
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