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.
Abstract
The aim of this study was to prepare rebamipide ocular inserts in order to extend its release on the ocular surface for dry eye treatment. Solubility study was applied to the drug with or without l-arginine using different solvents. Solvent casting technique was used to prepare the inserts; l-arginine was used to solubilize the drug, hydroxypropyl methylcellulose grades (E5 and K15M) and poly ethylene glycol 200 were used as excipients. The inserts were evaluated for their physical and mechanical properties, moisture loss% and absorption %, surface pH, and in-vitro drug release. The use l-arginine exhibited an enhancement of rebamipide solubility in both deionized water and phosphate buffer (pH 7.4) by a
... Show MoreEmpirical equations for estimating thickening time and compressive strength of bentonitic - class "G" cement slurries were derived as a function of water to cement ratio and apparent viscosity (for any ratios). How the presence of such an equations easily extract the thickening time and compressive strength values of the oil field saves time without reference to the untreated control laboratory tests such as pressurized consistometer for thickening time test and Hydraulic Cement Mortars including water bath ( 24 hours ) for compressive strength test those may have more than one day.
Accountancy unit is looked is upon as unit that established for the purpose achieve it goals and programmers for unlimited time. Unless otherwise take place such as liquation whether voluntary or mandatory. Thus going concern logic is considered to be the logical foundation witch the familiar accounting principles are based upon. The future of a Company real its financial statues and position and the extent of it ability to face events in future. Hence the success and continuity its activities depend on the extent of the company activity to generate profits. And its ability to retain appropriate liquidity to serve its debts.
Therefore financial statements of the company consider to be on
... Show MoreThe Internet image retrieval is an interesting task that needs efforts from image processing and relationship structure analysis. In this paper, has been proposed compressed method when you need to send more than a photo via the internet based on image retrieval. First, face detection is implemented based on local binary patterns. The background is notice based on matching global self-similarities and compared it with the rest of the image backgrounds. The propose algorithm are link the gap between the present image indexing technology, developed in the pixel domain, and the fact that an increasing number of images stored on the computer are previously compressed by JPEG at the source. The similar images are found and send a few images inst
... Show MoreChitosan-schiff base with three different ratios of para-Dimethyl aminobenzaldehyde& chitosan Schiff base hydrogels have been prepared for controlled drug release study. The synthesized chitosan Schiff base and chitosan Schiff base hydrogel were characterized by FT-IR, UV-Visible, SEM, analysis. Swelling properties of the hydrogel were investigated at three different media pH (2, 7, 10). The swelling degree varied with the pH, amount of crosslinking agent glutaraldehyde and with the amount of paraDimethylaminobenzaldehyde for the hydrogels. All hydrogels were used for controlled drug release system. Aspirin was used as model drug, in three different buffer solution (2, 7, 10) as release media. The rate of release of drugs in the pH2 is m
... Show MoreThe PbSe alloy was prepared in evacuated quarts tubs by the method of melt quenching from element, the PbSe thin films prepared by thermal evaporation method and deposited at different substrate temperature (Ts) =R.T ,373 and 473K . The thin films that deposited at room temperature (R.T=303)K was annealed at temperature, Ta= R.T, 373 and 473K . By depended on D.C conductivity measurements calculated the density of state (DOS), The density of extended state N(Eext) increases with increasing the Ts and Ta, while the density of localized state N(Eloc) is decreased . We investigated the absorption coefficient (?) that measurement from reflection and transmission spectrum result, and the effect of Ts and Ta on it , also we calculated the tai
... Show MoreObjective: The study aims at assessing the food frequency intake and dietary habits for diabetic pregnant
women.
Methodology: A descriptive study is carried out for the period from November4th 2013 to August
25th 2014. A purposive "non-probability" sample of one hundred diabetic pregnant women is selected from
the Diabetic and Endocrine Center in Al-Amarha City. A questionnaire is developed as a tool of data
collection. Content validity of the study instrument is determined through panel of experts. Split-half
reliability technique is used for reliability determination of the study instrument which depicts a reliability
coefficient of (0.79) for the entire scale. A structured interview with each diabetic pregnant wom