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Direct and inverse source problems for degenerate parabolic equations
Abstract<p>Degenerate parabolic partial differential equations (PDEs) with vanishing or unbounded leading coefficient make the PDE non-uniformly parabolic, and new theories need to be developed in the context of practical applications of such rather unstudied mathematical models arising in porous media, population dynamics, financial mathematics, etc. With this new challenge in mind, this paper considers investigating newly formulated direct and inverse problems associated with non-uniform parabolic PDEs where the leading space- and time-dependent coefficient is allowed to vanish on a non-empty, but zero measure, kernel set. In the context of inverse analysis, we consider the linear but ill-posed identification of a space-dependent source from a time-integral observation of the weighted main dependent variable. For both, this inverse source problem as well as its corresponding direct formulation, we rigorously investigate the question of well-posedness. We also give examples of inverse problems for which sufficient conditions guaranteeing the unique solvability are fulfilled, and present the results of numerical simulations. It is hoped that the analysis initiated in this study will open up new avenues for research in the field of direct and inverse problems for degenerate parabolic equations with applications.</p>
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Publication Date
Wed Mar 27 2019
Journal Name
Iraqi Journal Of Science
Application of Source Parameter Imaging (SPI) Technique to Gravity and Magnetic Data to Estimate the Basement Depth in Diyala Area, Eastern Central Iraq

The Bouguer gravity and magnetic RTP data were used to detect the depth of basement rocks in middle and south Diyala Province, east Iraq. The depth of the basement rocks was calculated by using the Source Parameter Imaging (SPI) method. New attempt is achieved to applied the SPI technique to the gravity values to estimate the depth of basement rocks. The depths of basement map derived from gravity data range 8-14 km, the depth of basement map derived from magnetic data range 9-13.5 km and the basement depth prepared by C.G.G, 1974 range 9-11 km. The derived maps from SPI method and that prepared by C.G.G, 1974 show good matching in the distribution of the depths of the study area. This study showed that basement’s depth range from

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Publication Date
Sun Jul 01 2012
Journal Name
Baghdad University College Of Education Ibn Al-haitham
Numerical Solution of Linear System of Fredholm Integral Equations Using Haar Wavelet Method

The aim of this paper is to present the numerical method for solving linear system of Fredholm integral equations, based on the Haar wavelet approach. Many test problems, for which the exact solution is known, are considered. Compare the results of suggested method with the results of another method (Trapezoidal method). Algorithm and program is written by Matlab vergion 7.

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Publication Date
Fri Jun 23 2023
Journal Name
Journal The College Of Basic Education / Al-mustansiriyah University
Numerical Solution of Non-linear Delay Differential Equations Using Semi Analytic Iterative Method

We present a reliable algorithm for solving, homogeneous or inhomogeneous, nonlinear ordinary delay differential equations with initial conditions. The form of the solution is calculated as a series with easily computable components. Four examples are considered for the numerical illustrations of this method. The results reveal that the semi analytic iterative method (SAIM) is very effective, simple and very close to the exact solution demonstrate reliability and efficiency of this method for such problems.

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Publication Date
Sat Jan 01 2022
Journal Name
International Journal Of Nonlinear Analysis And Applications
A general solution of some linear partial differential equations via two integral transforms

In this paper, a new analytical method is introduced to find the general solution of linear partial differential equations. In this method, each Laplace transform (LT) and Sumudu transform (ST) is used independently along with canonical coordinates. The strength of this method is that it is easy to implement and does not require initial conditions.

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Publication Date
Sun Jun 23 2019
Journal Name
Journal Of The College Of Basic Education
Numerical Solution of Non-linear Delay Differential Equations Using Semi Analytic Iterative Method

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Publication Date
Wed Jul 20 2022
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
On the Growth of Solutions of Nonhomogeneous Higher order Complex Linear Differential Equations

The nonhomogeneous higher order linear complex differential equation (HOLCDE) with meromorphic (or entire) functions is considered in this paper. The results are obtained by putting some conditions on the coefficients to prove that the hyper order of any nonzero solution of this equation equals the order of one of its coefficients in case the coefficients are meromorphic functions. In this case, the conditions were put are that the lower order of one of the coefficients dominates the maximum of the convergence exponent of the zeros sequence of it, the lower order of both of the other coefficients and the nonhomogeneous part and that the solution has infinite order. Whiles in case the coefficients are entire functions, any nonzero solutio

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Publication Date
Mon Mar 29 2021
Journal Name
Journal Of Engineering
Experimental Investigation of Thermal Performance of Aluminum Foil Coated with Polyester in a Direct Evaporative Cooling System

An experimental study was carried out for an evaporative cooling system in order to investigate the effect of using an aluminum pad coated with fabric polyester. In the present work, it was considered to use a new different type of cooling medium and test its performance during the change in the wet-bulb temperature and dry-bulb temperature of the supply air outside of the pad, the relative humidity of the supply air, the amount of air supplied (300-600) CFM and also the change of the amount of circulated water (1.75, 2.5, 4.5) liter per minute. A decrease in the WBT of the air was obtained, whereas the WBT of the air entering the pad was 26.5 . In contrast, the WBT of the outside air had reached 23  even though eva

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Publication Date
Sun Oct 30 2022
Journal Name
Iraqi Journal Of Science
Measurement of Absorbed Dose in Water Using Co-60 gamma source Teletherapy Units According to IAEA Dosimetry Protocols

      Modern radiotherapy facilities like 3-Dimensional conformal radio therapy (3DCRT), Intensity Modulated Radiotherapy (IMRT), were recently suggested in Co-60 machine with Multi-leaf Collimator (MLC). In this study, two reference chambers NE-2571#1205 and NE2581#537 were used for absolute dose measurement in Equinox accelerator. A comparison of dose measurement by two different IAEA protocols TRS-277 and TRS-398 has been studied. Analyzing TRS-398, a common shaped empirical formula was developed for the four Co-60 units of four Medical Colleges in Bangladesh with fitting parameters. It was found that an average discrepancy in the determination of absorbed dose in water among the two different protocols TRS-277 and TRS-398 were 1

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Publication Date
Mon Jan 28 2019
Journal Name
Iraqi Journal Of Science
Calibration of a Three Meter Small Radio Telescope in Baghdad University using the Sun as a Reference Source

The calibration of the three meter Baghdad University Radio Telescope (BURT) has been performed using two types of calibrations: Antenna Position calibration, and Detector calibration. The sun is used as a reference source to calibrate the telescope. The antenna position Azimuth (Az), and Elevation (El) are calibrate according to sun's azimuth and elevation in the date (11/10/2017; at time 10:19 AM). A calibration report is designed to illustrate the calibration parameters for each specific date and time. The detector calibration is representing a study for power spectrum response for the sun according to radio telescope frequency band (1.3 GHz – 1.5 GHz) with central frequency (1.42 GHz). Drift Scan function in the telescope's softwar

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Publication Date
Sun Mar 09 2025
Journal Name
Al–bahith Al–a'alami
The Reliance of the Public of Baghdad on News Broadcasts on Satellite Channels as a Source of Information

The importance of news broadcasts in society has increased after the domination of television over the mass media, especially after emerging the satellite channels, and spreading the satellite dishes among the public at large.

As well as the great role played by the modern technology in the transmission of news and events happening at once. Such role has contributed, significantly, in changing the concept and values ​​of the news. The live broadcast of the events filmed is the news itself.

In the midst of the great transformations and circumstances that Iraq went through after 2003, which witnessed political and security instability, and the large increase in the number of media, especially satellite channels, in Iraq

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