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.
Tested effective Alttafaria some materials used for different purposes, system a bacterial mutagenesis component of three bacterial isolates belonging to different races and materials tested included drug Briaktin
content Analysis for Some Type of Pillows used in Iraqi houses
The research aims to find ways to minimize the use of quantities of chemical fertilizers in agriculture in order to get to an environment that is free of contaminants. Magnetized water technology used in the experience of planting seeds of tomatoes Thomson type to obtain a higher efficiency to absorb fertilizer NRK in the protected environment of the period from February to June. Magnetized water system used locally made levels Gaues (4800,2500,1500) concentrations of 50 to 100% for each level and the rate of (4) replicates, and results indicated that the severity of the magnet (4800 Gaues) and a concentration of 50% gave the highest percentage of tomato fruit size and intensity ( 1500 Gaues) and a concentration of 100% did not give any inc
... Show MoreBackground: Surface treatment of machined dental zirconia for enhancement of the adhesion to resin cement, using Er,Cr:YSGG Laser. Materials and Methods: Total number of 42 zirconia disc specimens (9 mm diameter, and 2 mm height) was sintered according to the manufacturer instruction. They are divided into six groups, each group of seven samples. Laser groups (Experiment parameters) were depend on laser total irradiation time, pulse duration, and power. Group (A): 20 sec., 60 µs pulse duration. Group (B): 30 sec., 60 µs pulse duration. Group (C): 40 sec., 60 µs pulse duration. Group (D): 20 sec., 700 µs pulse duration. Group (E): 30 sec., 700 µs pulse duration, with different powers used (1, 1
... Show MoreCorrosion Resistance Enhancement for low carbon steel is very important to extend its life service, the coating process is one of the methods which can using to achieve this, and it's the most important in surface treatments to improve the properties of metals and alloys surfaces such as corrosion resistance. In this work, low carbon steel was nitrided and coated with nano zinc using gas phase coating technical, to enhance the resistance of corrosion. The process included adding two layers. The first, a nitride layer, was added by precipitating nitrogen (N) gas, and the second, a zinc (Zn) layer, was added by precipitating Zn. The process of precipitating was carried out at different periods (5, 10, and 15 minutes). Scan electron mi
... Show MoreThe Russian foreign policy of the post-cold-war era faced dilemmas in the light of the international and regional realities of the disintegration of the Soviet Union and the formation of a new unipolar international order led by the United States of America. Thus, Russian foreign policy-making was divided over the nature of the foreign policy to be followed. The achievement of the Russian goals, especially as the objectives of Russian foreign policy have been set within the framework of trying to regain the status and leading role, as well as the establishment of some fundamental changes to be consistent with the new international situation of the post-one The Russian Federation has adopted in the sphere of its foreign policy to the vari
... Show MoreThe researcher highlighted in his research on an important subject that people need, which is the excuse of ignorance in Islamic law. , As the flag of light and ignorance of darkness. Then the researcher lameness of the reasons for research in this subject as it is one of the assets that should be practiced by the ruler and the judge and the mufti and the diligent and jurisprudent, but the public should identify the issues that ignore ignorance and issues that are not excused even if claimed ignorance.
Then the researcher concluded the most important results, and recommendations that he wanted to set scientific rules for students of science and Muslims in general, to follow the issues of legitimacy and learn its provisions and i