Second-order differential inclusions with two small parameters

Consider in a real Hilbert space H the following problem, denoted (Pɛμ), −ɛu′′(t)+μu′(t)+Au(t)+Bu(t)∋f(t),00,μ≥0 are small parameters, A:D(A)⊂H→H is a maximal monotone operator (possibly multivalued), and B:H→H is a Lipschitz operator (or monotone and Lipschitz on bounded sets). Consider also the fo...

Full description

Saved in:
Bibliographic Details
Published in:Nonlinear analysis: real world applications 2024-06, Vol.77, p.104061, Article 104061
Main Authors: Barbu, Luminiţa, Moroşanu, Gheorghe, Vîntu, Ioan Vladimir
Format: Article
Language:English
Subjects:
Approximation
Heat equation
Lions regularization
Lipschitz operator
Maximal monotone operator
Telegraph differential system
Citations: Items that this one cites
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:Consider in a real Hilbert space H the following problem, denoted (Pɛμ), −ɛu′′(t)+μu′(t)+Au(t)+Bu(t)∋f(t),00,μ≥0 are small parameters, A:D(A)⊂H→H is a maximal monotone operator (possibly multivalued), and B:H→H is a Lipschitz operator (or monotone and Lipschitz on bounded sets). Consider also the following reduced problem, denoted (Pμ), μu′(t)+Au(t)+Bu(t)∋f(t),00 and μ≥0; (c) convergence of the solution of problem (Pɛμ) to the solution of problem Pμ0, as ɛ→0+ and μ→μ0, where μ0 is a fixed positive number; (d) convergence of the solution of problem (Pɛμ) to the solution of the equation Au+Bu∋f(t) as ɛ→0+ and μ→0+; (e) applications.
ISSN:1468-1218
1878-5719
DOI:10.1016/j.nonrwa.2024.104061