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Register a new userUsing some Functional Analysis methods in studying small motions of Hydrodynamicssystem
استخدام بعض طرائق التحليل التابعي في دراسة الحركات الصغيرة لجملة هيدروديناميكية
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Tishreen University ورقة بحثية
Publication date
2014
fields
Mathematics
and research's language is
العربية
Created by
Shamra Editor
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يُعنى هذا البحث بدراسة الحركات الصغيرة لمجموعة من السوائل اللزجة الشعرية في أنبوب دوراني ,أي البرهان على وجود ووحدانية حل لمسألة القيمة الحدّية الابتدائية التي تصف هذه الحركات ، من خلال تحويل المسألة إلى مسألة كوشي لها الشكل الآتي: حيث دالّة مستمرة تأخذ قيمها في فضاء هلبرت و مؤثر معرف في هذا الفضاء, وذلك باستخدام طرائق في التحليل التابعي ( مثل الإسقاط المعامد, مقاربة مؤثر,....)
This Work suggests a study of small motions of system of capillary viscous fluids in rotation vessels ,i.e: to prove the unique solvability theorem of the initial boundary value problem that describe these motions. For that we reduced to Cauchy problem that has the form: Where is a continuous function with values in the Hilbert space E, A is an operator on E, By using Functional analysis methods (Orthogonal projector, Operator approach,…)
References used
KOPACHEVSKY,N.D; KREIN,S.G; NGO ZUY CAN. Operators Methods in Linear Hydrodynamics:Evolution and Spectral Problems. Nauka, Moscow, 1989,159-181
OPACHEVSKY,N.D; KREIN,S.G .Operator Approach in Linear Problems of Hydrodynamics Vol. 1: Self-adjoint Problems for Ideal Fluid, Birkh¨auserVerlag, Basel—Boston—Berlin, 2001,383
KOPACHEVSKY,N.D; KREIN,S.G. Operator Approach in Linear Problems of Hydrodynamics.Vol. 2: Nonself-adjoint Problems for Viscous Fluids, Birkh¨auserVerlag, Basel—Boston—Berlin, 2003, 444
KOPACHEVSKY,N.D. On Stability and Instability of small motions of Hydrodynamicalsystems,Methods of Functional Analysis and topology,Vol. 13 (2007), no. 2, 152–168
(SUSLINA,T.A. Spectral asymptotics of two prototype problems on oscillations of fluids, Iz. St.PetersburgElectrotechn. Inst., 449, 82–88 (1992
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