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TWO-PARAMETER SECOND-ORDER DIFFERENTIAL INCLUSIONS IN HILBERT SPACES.
- Source :
-
Annals: Series on Mathematics & its Applications . 2020, Vol. 12 Issue 1/2, p274-294. 21p. - Publication Year :
- 2020
-
Abstract
- In a real Hilbert space H, let us consider the boundary-value problem -εu"(t) + βu'(t) + Au(t) + Bu(t) ∋ f(t), t ∈ [0; T]; u(0) = u0, u'(T) = 0, where T > 0 is a given time instant, ε,μ are positive parameters, A: D(A) ⊂ H → H is a (possibly set-valued) maximal monotone operator, and B: H → H is a Lipschitz operator. In this paper, we investigate the behavior of the solutions to this problem in two cases: (i) μ > 0 fixed, 0 < ε → 0, and (ii) ε > 0 fixed and 0 < μ → 0. Notice that if μ = 1 and ε is a positive small parameter, the above problem is a Lions-type regularization of the Cauchy problem u0(t) + Au(t) + Bu(t) ∋ f(t); t 2 [0; T]; u(0) = u0, which was recently studied by L. Barbu and G. Moroşanu [Commun. Contemp. Math. 19 (2017)]. Our abstract results are illustrated with examples related to the heat equation and the telegraph differential system. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 20665997
- Volume :
- 12
- Issue :
- 1/2
- Database :
- Academic Search Index
- Journal :
- Annals: Series on Mathematics & its Applications
- Publication Type :
- Academic Journal
- Accession number :
- 147850592