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.
In this paper, a sufficient condition for stability of a system of nonlinear multi-fractional order differential equations on a finite time interval with an illustrative example, has been presented to demonstrate our result. Also, an idea to extend our result on such system on an infinite time interval is suggested.
In this work, a novel technique to obtain an accurate solutions to nonlinear form by multi-step combination with Laplace-variational approach (MSLVIM) is introduced. Compared with the traditional approach for variational it overcome all difficulties and enable to provide us more an accurate solutions with extended of the convergence region as well as covering to larger intervals which providing us a continuous representation of approximate analytic solution and it give more better information of the solution over the whole time interval. This technique is more easier for obtaining the general Lagrange multiplier with reduces the time and calculations. It converges rapidly to exact formula with simply computable terms wit
... Show MoreThis study was conducted in the Tissue Culture laboratory of the Horticultural Department of the Faculty of Agriculture at Karbala University to investigate the effects of a light source (Florescent, LED) and adenine sulfate (Ads) a 0, 40, 80, and 120 mg l-1 on the multiplication and rooting of
Digital Elevation Model (DEM) is one of the developed techniques for relief representation. The definition of a DEM construction is the modeling technique of earth surface from existing data. DEM plays a role as one of the fundamental information requirement that has been generally utilized in GIS data structures. The main aim of this research is to present a methodology for assessing DEMs generation methods. The DEMs data will be extracted from open source data e.g. Google Earth. The tested data will be compared with data produced from formal institutions such as General Directorate of Surveying. The study area has been chosen in south of Iraq (Al-Gharraf / Dhi Qar governorate. The methods of DEMs creation are kri
... Show MoreDigital Elevation Model (DEM) is one of the developed techniques for relief representation. The definition of a DEM construction is the modeling technique of earth surface from existing data. DEM plays a role as one of the fundamental information requirement that has been generally utilized in GIS data structures. The main aim of this research is to present a methodology for assessing DEMs generation methods. The DEMs data will be extracted from open source data e.g. Google Earth. The tested data will be compared with data produced from formal institutions such as General Directorate of Surveying. The study area has been chosen in south of Iraq (Al-Gharraf / Dhi Qar governorate. The methods of DEMs creation are kriging, IDW (inver
... Show MoreThis research studies the influence of water source on the compressive strength of high strength concrete. Four types of water source were adopted in both mixing and curing process these are river, tap, well and drainage water (all from Iraq-Diyala governorate). Chemical analysis was carried out for all types of the used water including (pH, total dissolved solids (TDS), Turbidity, chloride, total suspended solid (TSS), and sulfates). Depending on the chemical analysis results, it was found that for all adopted sources the chemical compositions was within the ASTM C 1602/C 1602M-04 limits and can be satisfactorily used in concrete mixtures. Mixture of high strength concrete for compressive strength of (60 MPa) was designed and checked using
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