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Direct and inverse source problems for degenerate parabolic equations
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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
Mon Oct 01 2012
Journal Name
Computers &amp; Mathematics With Applications
Boundary element formulations for the numerical solution of two-dimensional diffusion problems with variable coefficients
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Publication Date
Wed Aug 01 2018
Journal Name
Journal Of Economics And Administrative Sciences
Proposed Measure for Effect Size in Mediation Analysis with Solution to Some Mediation Process Problems
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In this paper, the effect size measures was discussed, which are useful in many estimation processes for direct effect and its relation with indirect and total effects. In addition, an algorithm to calculate the suggested measure of effect size was suggested that represent the ratio of direct effect to the effect of the estimated parameter using the Regression equation of the dependent variable on the mediator variable without using the independent variable in the model. Where this an algorithm clear the possibility to use this regression equation in Mediation Analysis, where usually used the Mediator and independent variable together when the dependent variable regresses on them. Also this an algorithm to show how effect of the

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Publication Date
Mon Mar 08 2021
Journal Name
Baghdad Science Journal
An approximate solution for solving linear system of integral equation with application on "Stiff" problems
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An approximate solution of the liner system of ntegral cquations fot both fredholm(SFIEs)and Volterra(SIES)types has been derived using taylor series expansion.The solusion is essentailly

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Publication Date
Tue Nov 13 2018
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
The Approximation Solution of a Nonlinear Parabolic Boundary Value Problem Via Galerkin Finite Elements Method with Crank-Nicolson
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    This paper deals with finding the approximation solution of a nonlinear parabolic boundary value problem (NLPBVP) by using the Galekin finite element method (GFEM) in space and Crank Nicolson (CN) scheme in time, the problem then reduce to solve a Galerkin nonlinear algebraic system(GNLAS). The predictor and the corrector technique (PCT) is applied here to solve the GNLAS, by transforms it to a Galerkin linear algebraic system (GLAS). This GLAS is solved once using the Cholesky method (CHM) as it appear in the matlab package and once again using the Cholesky reduction order technique (CHROT) which we employ it here to save a massive time. The results, for CHROT are given by tables and figures and show

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Publication Date
Wed Jan 01 2014
Journal Name
The Scientific World Journal
Heat Transfer Enhancement of Laminar Nanofluids Flow in a Circular Tube Fitted with Parabolic-Cut Twisted Tape Inserts
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Numerical investigation has been carried out on heat transfer and friction factor characteristics of copper-water nanofluid flow in a constant heat-fluxed tube with the existence of new configuration of vortex generator using Computational Fluid Dynamics (CFD) simulation. Two types of swirl flow generator: Classical twisted tape (CTT) and Parabolic-cut twisted tape (PCT) with a different twist ratio (y= 2.93, 3.91 and 4.89) and different cut depth (w= 0.5, 1.0 and 1.5 cm) with 2% and 4% volume concentration

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Publication Date
Tue May 01 2018
Journal Name
Journal Of Physics: Conference Series
Photoluminescence Spectra From The Direct Energy Gap of a-SiQDs
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Publication Date
Mon Mar 04 2024
Journal Name
Journal Of Engineering
REMOVAL OF DIRECT BLUE DYE IN TEXTILEWASTEWATER EFFLUENT BY ELECTROCOAGULATION
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 Removal of direct blue dye by electrocoagulation method has been investigated using aluminum   electrode in a bench-scale electrochemical system. Current density, NaCl concentration,   electrocoagulation time, and dye concentration has been studied as effecting parameters in color   removal efficiency. Increasing of current density will increase the color removal efficiency and   energy consumption as well. While increasing NaCl concentration increase the color removal   efficiency but it decrease energy consumption. High dye concentration is needed for extra   electrocaogolation time to reach the same efficiency that obtained with low dye concentration .With   current applied 0.35 amps. and NaCl concentration of 2 g/l more

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Publication Date
Tue Dec 30 2014
Journal Name
Iraqi Journal Of Chemical And Petroleum Engineering
Performance Evaluation of Three Phase Spray Direct Contact Heat Exchanger
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The present investigation deals with experimental study of three-phase direct-contact heat exchanger, for water-Freon R11 system, where water is the continuous phase (liquid) and Freon R11 (liquid-gas) is the dispersed phase. The test section consisted of a cylindrical Perspex column with inner diameter 8cm and 1.2m long, in which, water was to be confined. Liquid Freon R11 drops were injected into the hot water filled column, through a special design of distributors at the bottom of the column. The liquid Freon R11 drops rose on their way up and evaporated into two-phase bubbles at atmospheric pressure. The study was devoted to express the effect of process variables such as c

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Publication Date
Thu Feb 01 2018
Journal Name
Applied Mathematical Modelling
Identification of a multi-dimensional space-dependent heat source from boundary data
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Publication Date
Wed Jan 01 2020
Journal Name
Materials Today: Proceedings
Biomaterial composition of the microalga Coelastrella sp. (MH923012): Effect of carbon source
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