希尔伯特空间中的双参数二阶微分包含

Q4 Mathematics Annals of the Academy of Romanian Scientists: Series on Mathematics and its Applications Pub Date : 2020-01-01 DOI:10.56082/annalsarscimath.2020.1-2.274

G. Moroşanu, A. Petruşel

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引用次数: 0

摘要

在实数Hilbert空间H中，考虑边值问题εu00(t) + μ u0 (t) + Au(t) + Bu(t) 3f (t)， t∈[0,t];u(0) = u0, u0 (T) = 0，其中T > 0是给定的时间瞬间，ε、µ是正参数，a: D(a)∧H→H是一个(可能是集值的)极大单调算子，B: H→H是一个Lipschitz算子。本文研究了这一问题在两种情况下解的性质:(i)µ> 0固定，0 < ε→0，以及(ii) ε > 0固定，0 <µ→0。注意，如果µ= 1且ε是一个正的小参数，则上述问题是Cauchy问题u 0 (t) + Au(t) + Bu(t) 3f (t)， t∈[0,t]的lions型正则化;u(0) = 0，这是最近由L. Barbu和G. Moro & sanu [common]研究的。一栏。数学，19 (2017)[j]。用热方程和电报微分系统的例子说明了我们的抽象结果。

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TWO-PARAMETER SECOND-ORDER DIFFERENTIAL INCLUSIONS IN HILBERT SPACES

In a real Hilbert space H, let us consider the boundary-value problem −εu00(t) + µu0 (t) + Au(t) + Bu(t) 3 f(t), t ∈ [0, T]; u(0) = u0, u0 (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 u 0 (t) + Au(t) + Bu(t) 3 f(t), t ∈ [0, T]; u(0) = u0, which was recently studied by L. Barbu and G. Moro¸sanu [Commun. Contemp. Math. 19 (2017)]. Our abstract results are illustrated with examples related to the heat equation and the telegraph differential system.

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来源期刊

Annals of the Academy of Romanian Scientists: Series on Mathematics and its Applications Mathematics-Mathematics (all)

CiteScore

0.60

自引率

0.00%

发文量

审稿时长

25 weeks

期刊介绍： The journal Mathematics and Its Applications is part of the Annals of the Academy of Romanian Scientists (ARS), in which several series are published. Although the Academy is almost one century old, due to the historical conditions after WW2 in Eastern Europe, it is just starting with 2006 that the Annals are published. The Editor-in-Chief of the Annals is the President of ARS, Prof. Dr. V. Candea and Academician A.E. Sandulescu (†) is his deputy for this domain. Mathematics and Its Applications invites publication of contributed papers, short notes, survey articles and reviews, with a novel and correct content, in any area of mathematics and its applications. Short notes are published with priority on the recommendation of one of the members of the Editorial Board and should be 3-6 pages long. They may not include proofs, but supplementary materials supporting all the statements are required and will be archivated. The authors are encouraged to publish the extended version of the short note, elsewhere. All received articles will be submitted to a blind peer review process. Mathematics and Its Applications has an Open Access policy: all content is freely available without charge to the user or his/her institution. Users are allowed to read, download, copy, distribute, print, search, or link to the full texts of the articles in this journal without asking prior permission from the publisher or the author. No submission or processing fees are required. Targeted topics include : Ordinary and partial differential equations Optimization, optimal control and design Numerical Analysis and scientific computing Algebraic, topological and differential structures Probability and statistics Algebraic and differential geometry Mathematical modelling in mechanics and engineering sciences Mathematical economy and game theory Mathematical physics and applications.