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Well-posedness of inverse problems for systems with time dependent parameters
Joint Authors
Source
The Arabian Journal for Science and Engineering. D, Mathematics
Issue
Vol. 34, Issue 1D (31 May. 2009), pp.39-58, 20 p.
Publisher
King Fahd University of Petroleum and Minerals
Publication Date
2009-05-31
Country of Publication
Saudi Arabia
No. of Pages
20
Main Subjects
Topics
Abstract AR
سنفحص في هذه الورقة النموذج الزائدي المجرد ذا الجساءة و الكبح.
المعتمدين على الزمن و المعطى بـ {ü (t), ψ} v*, v + d (t ; u˙(t), ψ) + a(t ;u (t), ψ) = { f (t), ψ} v*,v حيث V ⊂ VD ⊂ H ⊂ VD* ⊂ V* هي فضاءات هيلبرت مع حقن مستمر و كثيف، و حيث تنطبق H مع ثَنويها، و ترمز {.,.} إلى الضرب الثنَوي المزامل.
سنثبت، تحت شروط معقولة على الصيغتين المعتمدتين على الزمن a {t, .,.} : V x V → C و d {t, .,.} : VD x VD → C (كلتاهما خطية و نصف)، إن هذا النموذج يسمح بحل وحيد و إن هذا الحل يعتمد على معطيات المسألة بطريقة مستمرة.
سوف ندرس أيضاً مسألة جودة الصيغة و التقريبات من نوع العناصر المنتهية للمسائل العكسية المزاملة.
هذه المسألة هي صياغة ضعيفة تشمل نماذج المؤثرات التفاضلية المجردة و تندرج فيها معادلات الصفائح و العوارض و القشور مع عدة أنواع مهمة من الكبح.
Abstract EN
In this paper we investigate the abstract hyperbolic model with time dependent stiffness and damping given by h ¨ u(t);yiV;V +d(t; ˙ u(t);y)+a(t;u(t);y) = h f (t);yiV;V where V VD H V D V are Hilbert spaces with continuous and dense injections, where H is identified with its dual and h; i denotes the associated duality product.
We show under reasonable assumptions on the time-dependent sesquilinear forms a(t; ; ) : V V !C and d(t; ; ) :VDVD !C that this model allows a unique solution and that the solution depends continuously on the data of the problem.
We also consider well-posedness as well as finite element type approximations in associated inverse problems.
The problem above is a weak formulation that includes models in abstract differential operator form that include plate, beam and shell equations with several important kinds of damping.
American Psychological Association (APA)
Banks, H. T.& Pedersen, M.. 2009. Well-posedness of inverse problems for systems with time dependent parameters. The Arabian Journal for Science and Engineering. D, Mathematics،Vol. 34, no. 1D, pp.39-58.
https://search.emarefa.net/detail/BIM-546050
Modern Language Association (MLA)
Banks, H. T.& Pedersen, M.. Well-posedness of inverse problems for systems with time dependent parameters. The Arabian Journal for Science and Engineering. D, Mathematics Vol. 34, no. 1D (May. 2009), pp.39-58.
https://search.emarefa.net/detail/BIM-546050
American Medical Association (AMA)
Banks, H. T.& Pedersen, M.. Well-posedness of inverse problems for systems with time dependent parameters. The Arabian Journal for Science and Engineering. D, Mathematics. 2009. Vol. 34, no. 1D, pp.39-58.
https://search.emarefa.net/detail/BIM-546050
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references : p. 56-57
Record ID
BIM-546050