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.
The research aims to develop alternatives to transportation at the entrance to the Educational City (University of Baghdad) during the morning and evening peaks, which result from of the traffic congestion at the entrances to the educational city (the University of Baghdad), and affects the emotional, functional, and social performance of the whole city, and leads to hotbeds of confluence and congestion at the entrances in the morning and evening peaks. This movement was measured on the ground for pedestrians and vehicles. Some criteria were adopted to determine the density of road length to the area and density of roads for the number of users and the rate of the area served by roads. The research reviews the experiences of some
... Show MoreThe objective of the research is to identify the effect of an instructional design according to the active learning modelsالباحثين in the achievement of the students of the fifth grade, the instructional design was constructed according to the active learning models for the design of education. The research experience was applied for a full academic year (the first & the second term of 2017-2018). The sample consisted of 58 students, 28 students for the experimental group and 30 students for the control group. The experimental design was adopted with partial and post-test, the final achievement test consisted of (50) objectives and essays items on two terms, the validity of the test was verified by the adoption of the Kudoric
... Show MoreThe Anticyclone Merge affects Iraq’s climate clearly through its impact on the different climatic elements. where it appears while they pass through special and distinctive weather . and most of this affection appears in temperatures, Therefore, this research study the relationship between the repetition and the survival period of the Anticyclone Merge and temperature average by using coefficient correlation (Pearson) that shows there’s strong inverse relationship between the integration of Anticyclones and temperatures average. &nbs
... Show MoreMost of the studies conducted in the past decades focused on the effect of interest rates and exchange rates on domestic investment under the assumption that the independent variables have the same effect on the dependent variable, but there were limited studies that investigated the unequal effects of changes in interest rates and exchange rates, both positive and negative, on domestic investment. This study used a nonlinear autoregressive distributed lag (NARDL) model to assess the unequal effects of the real interest rate and real exchange rate variables on domestic investment in Egypt for the period 1976 - 2020. The results revealed that positive and negative shocks for both exchange rates have unequal effects on
... Show MorePurpose: To identify the size of the food gap for the main agricultural products and crops in Iraq, which reflects to us the extent to which agricultural production in particular and the agricultural sector in general have declined.Theoretical framework: The theoretical side of the research dealt with the definition of self-sufficiency and the food gap, as well as identifying the reality of agricultural production in Iraq during the study period, as well as the reality of the food gap for the most important agricultural, plant and animal products.Design/methodology/approach: In reviewing the research problem, the researcher adopted the method of deductive and descriptive analysis based on the presentation and detail of official data
... Show MoreThe mechanism for selecting the President of the Republic and his constitutional powers under the Constitution of the Republic of Iraq
The ability of four local fungal isolates for extracellular laccase production has been tested with five grams 1:1(w/v) humidified sawdust as substrate in mineral salt medium. After 21 day of incubation at 25±1 ? C and using one mycelial plug (5mm), higher level of laccase activity (0.15U/ml) and specific activity (15U/mg) were observed by Pleurotus ostreatus in comparison with other fungal isolates. The results of optimum conditions for laccase production from selected isolate showed that, the maximum laccase activity (0.55U/ml) and specific activity (55U/mg) were obtained at moisture ratio 1:3 (w/v), using 3 mycelial plugs (5 mm), after 15 days incubation period at 25±1 ? C. The results of phenol degradation by crud laccase revealed th
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