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.
Iraqi EFL teachers face problems in teaching “English for Iraq Series” for primary public school pupils. In this paper, the researchers are going to identify the main problems faced by our teachers and try to find solutions to these problems. To achieve the aim of the study, list of questions asked and from teachers’ responses, the researchers have got an idea about the main problems which are related to textbook material, parents, learners, environment and technology. Therefore, the researchers adapted a questionnaire to achieve the purpose of the study with some changes and modifications. This questionnaire with five point scale (strongly agree, agree, undecided, disagree, strongly disagree). To achieve face validity, the
... Show MorePhysics and applied mathematics form the basis for understanding natural phenomena using differential equations depicting the flow in porous media, the motion of viscous liquids, and the propagation of waves. These equations provide a thorough study of physical processes, enhancing the understanding of complex applications in engineering, technology, and medicine. This paper presents novel approximate solutions for the Darcy-Brinkmann-Forchheimer moment equation, the Blasius equation and the FalknerSkan equation with initial / boundary conditions by using two iterative methods: the variational iteration method and the optimal variational iteration method. The variational iteration method is effectively developed by adding a control paramete
... Show MoreThis paper aims to find new analytical closed-forms to the solutions of the nonhomogeneous functional differential equations of the nth order with finite and constants delays and various initial delay conditions in terms of elementary functions using Laplace transform method. As well as, the definition of dynamical systems for ordinary differential equations is used to introduce the definition of dynamical systems for delay differential equations which contain multiple delays with a discussion of their dynamical properties: The exponential stability and strong stability
abstract:
The aim of this study is to clarify the relationship between the concept of inconsistency and the measurement of the inverse relationship of overlap and contrast. The study will address the following points:
- Explaining the true nature of inconsistency and contrast, as understanding their relationship is essential for determining them.
- Examining the view of the scholars regarding their significance as approaches to understanding the relationship.
- Identifying the relationship between inconsistency and contrast in terms of overlap and contrast.
Shumblan (SH) is one of the most undesirable aquatic plants widespread in the irrigation channels and water bodies. This work focuses on boosting the biogas potential of shumblan by co-digesting it with other types of wastes without employing any chemical or thermal pretreatments as done in previous studies. A maximum biogas recovery of 378 ml/g VS was reached using shumblan with cow manure as inoculum in a ratio of 1:1. The methane content of the biogas was 55%. Based on volatile solid (VS) and C/N ratios, biogas productions of 518, 434, and 580 ml/g VS were obtained when the shumblan was co-digested with food wastes (SH:F), paper wastes (SH:P), and green wastes (SH:G) respectively. No significant changes of methane contents were observ
... Show MoreIn this paper, simulation studies and applications of the New Weibull-Inverse Lomax (NWIL) distribution were presented. In the simulation studies, different sample sizes ranging from 30, 50, 100, 200, 300, to 500 were considered. Also, 1,000 replications were considered for the experiment. NWIL is a fat tail distribution. Higher moments are not easily derived except with some approximations. However, the estimates have higher precisions with low variances. Finally, the usefulness of the NWIL distribution was illustrated by fitting two data sets
The present study dealt with the removal of methylene blue from wastewater by using peanut hulls (PNH) as adsorbent. Two modes of operation were used in the present work, batch mode and inverse fluidized bed mode. In batch experiment, the effect of peanut hulls doses 2, 4, 8, 12 and 16 g, with constant initial pH =5.6, concentration 20 mg/L and particle size 2-3.35 mm were studied. The results showed that the percent removal of methylene blue increased with the increase of peanut hulls dose. Batch kinetics experiments showed that equilibrium time was about 3 hours, isotherm models (Langmuir and Freundlich) were used to correlate these results. The results showed that the (Freundlich) model gave the best fitting for adsorption capacity. D
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