On the regularization of solution of an inverse ultraparabolic equation associated with perturbed final data ... : حول تنظيم حل معادلة عكسية فائقة القطع المكافئ مرتبطة بالبيانات النهائية المضطربة ...

In this paper, we study the inverse problem for a class of abstract ultraparabolic equations which is well-known to be ill-posed. We employ some elementary results of semi-group theory to present the formula of solution, then show the instability cause. Since the solution exhibits unstable dependenc...

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Bibliographic Details
Main Authors: Nguyen Huy Tuan, Vo Anh Khoa, Le Trong Lan, Tran The Hung
Format: Text
Language:English
Published: OpenAlex 2015
Subjects:
Inverse Problems in Mathematical Physics and Imaging
Mathematical Physics
FOS Mathematics
Mathematics
Physical Sciences
Multiscale Methods for Heterogeneous Systems
Computational Theory and Mathematics
Computer Science
Arctic Sea Ice Variability and Decline
Atmospheric Science
Earth and Planetary Sciences
Inverse Problems
Regularization Methods
Ill-Posed Problems
Regularization linguistics
Inverse problem
Inverse
Applied mathematics
Instability
Mathematical analysis
Computer science
Physics
Artificial intelligence
Mechanics
Geometry
Sea ice
Online Access:https://dx.doi.org/10.60692/7zakb-d4g78
https://gresis.osc.int//doi/10.60692/7zakb-d4g78
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Summary:In this paper, we study the inverse problem for a class of abstract ultraparabolic equations which is well-known to be ill-posed. We employ some elementary results of semi-group theory to present the formula of solution, then show the instability cause. Since the solution exhibits unstable dependence on the given data functions, we propose a new regularization method to stabilize the solution. then obtain the error estimate. A numerical example shows that the method is efficient and feasible. This work slightly extends to the earlier results in Zouyed et al. \cite{key-9} (2014). ... : في هذه الورقة، ندرس المسألة العكسية لفئة من المعادلات فوق القطعية المجردة المعروفة بسوء وضعها. نستخدم بعض النتائج الأولية لنظرية شبه المجموعة لتقديم صيغة الحل، ثم إظهار سبب عدم الاستقرار. نظرًا لأن الحل يظهر اعتمادًا غير مستقر على وظائف البيانات المعطاة، فإننا نقترح طريقة تنظيم جديدة لتثبيت الحل. ثم الحصول على تقدير الخطأ. يوضح مثال رقمي أن الطريقة فعالة ومجدية. يمتد هذا العمل قليلاً إلى النتائج السابقة في Zouyed et al. \cite{key -9} (2014). ...

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