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 oil crudes have some of the physical and chemical characteristics that distinguish it from other types of oil crudes in the world. Some of these features such us molecular composition, rheological, viscosity and emulsions are studied carefully by researchers. In this work, a comparative study of the linear and the non-linear optical properties for typical heavy and light crude oils of Iraqi origin was studied utilizing Z-scan technique. The He -Ne laser of wavelength 632.8 nm had been used for this purpose. These samples were collected from Basra and Kut oil fields. The values of the non-linear refractive index (n2), non-linear absorption coefficient (β), and third-order electrical susceptibility (χ3) were e
... Show MoreBasketball is a popular game in many parts of the world and many developed countries are making continuous efforts to prepare and develop their emerging players on scientific and clear bases as the basis for reaching high levels The researchers used the descriptive approach in the method of correlative studies to suit the nature of the study The readymade software (IBM SPSS Statistics Version24) was used to perform statistical treatments The researchers concluded that there was a significant relationship between body size indicators (height and weight) with the fitness elements of the emerging basketball players The researchers recommended conducting a similar study to determine the type of relationship to the indicators of the physical str
... Show MoreThe research aims to apply the novel forward osmosis (FO) process to recover pure water
from contaminated water. Phenol was used as organic substance in the feed solution, while sodium
chloride salt was used as draw solution. Membranes used in the FO process is the cellulose
triacetate (CTA) and polyamide (thin film composite (TFC)) membrane. Reverse osmosis process
was used to treatment the draw solution, the exterior from the forward osmosis process. In the FO
process the active layer of the membrane faces the feed solution and the porous support layer faces
the draw solution and this will show the effect of dilutive internal concentration polarization and
concentrative external concentration polarization.
In th
Nanopesticides are novel plant protection products offering numerous benefits. Because nanoparticles behave differently from dissolved chemicals, the environmental risks of these materials could differ from conventional pesticides. We used soil–earthworm systems to compare the fate and uptake of analytical‐grade bifenthrin to that of bifenthrin in traditional and nanoencapsulated formulations. Apparent sorption coefficients for bifenthrin were up to 3.8 times lower in the nano treatments than in the non‐nano treatments, whereas dissipation half‐lives of the nano treatments were up to 2 times longer. Earthworms in the nano treatments accumulated approximately 50% more b
Future generations of wireless networks are expected to heavily rely on unmanned aerial vehicles (UAVs). UAV networks have extraordinary features like high mobility, frequent topology change, tolerance to link failure, and extending the coverage area by adding external UAVs. UAV network provides several advantages for civilian, commercial, search and rescue applications. A realistic mobility model must be used to assess the dependability and effectiveness of UAV protocols and algorithms. In this research paper, the performance of the Gauss Markov (GM) and Random Waypoint (RWP) mobility models in multi-UAV networks for a search and rescue scenario is analyzed and evaluated. Additionally, the two mobility models GM and RWP are descr
... Show MoreErosion and deposition are natural phenomena in many estuaries that can cause morphological changes, leading to navigation and offshore structure problems. Many previous studies have focused on investigating the morphological changes of estuaries depending on different parameters and their combined effects with erosion and deposition processes, such as maximum flow amplitude, waves, currents, tidal flow, storms, rising sea elevation, maximum turbidity, salinity, and bed roughness height as input parameters. These studies are based on field measurements and numerical simulations by using topographic surveys, soil samples, satellite images, geological data, and bathymetric maps with the aid of ArcGIS. Some of these studies examine the
... Show MoreThe experiment was conducted in Baghdad for study effect using mold board and disc plows as main factor , and second factor was three speeds 1.85 , 3.75 and 5.62 km / hr , and sub-second factor was three levels of soil moisture 21,18 and 14 % to determined data fuel consumption and economy costs machine unit in silt clay loam with depth 22cm. The experiment was a split – split plot arrangement in a randomized complete block design with three replications and statistical analysis using Least Significant Design 0.05 was used to compare the means of treatments. Mold board recorded least fuel consumption and cast fixed and variable and management and total costs of tractor and plow costs and total cost. Increasing forward speeds of the t
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