The compactness and the stability of the weak solution of nonautonomous maximal monotone flows are proved with respect to nonparametric perturbations of the operator. To this purpose the flow is formulated in weak form as a null-minimization problem, and De Giorgi's notion of Gamma-convergence is used. It is proved that all sequences of those flows have a Gamma-convergent subsequence, and that the Gamma-limit is also a maximal monotone flow and exhibits no long memory. These results can be applied to several quasilinear equations. (C) 2021 Published by Elsevier Inc.
Γ-compactness and Γ-stability of maximal monotone flows / Visintin, A.. - In: JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS. - ISSN 0022-247X. - 506:1(2022), p. 125602. [10.1016/j.jmaa.2021.125602]
Γ-compactness and Γ-stability of maximal monotone flows
Visintin, A.
2022-01-01
Abstract
The compactness and the stability of the weak solution of nonautonomous maximal monotone flows are proved with respect to nonparametric perturbations of the operator. To this purpose the flow is formulated in weak form as a null-minimization problem, and De Giorgi's notion of Gamma-convergence is used. It is proved that all sequences of those flows have a Gamma-convergent subsequence, and that the Gamma-limit is also a maximal monotone flow and exhibits no long memory. These results can be applied to several quasilinear equations. (C) 2021 Published by Elsevier Inc.| File | Dimensione | Formato | |
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