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.
Iraq has seen many changes at the social, economic and political levels. This led to cause many shifts in the structure of its society and imposed great challenges reflected in the behavior and awareness of that society in general and youth in particular.
Those changes made the Iraqi society undergoing the transformation of value and culture aspects formed a political awareness that caused cultural and political diversity within the family and society. A greater openness to the outside world caused by the communication revolution, as the world has witnessed during the past two decades, has helped in making that change. Iraq had its share of media and political openness, which were included after the US occupation in 2003. As a re
... Show MoreIn a world of fierce competition companies of different activities strive to strengthen their competitiveness in order to be able to deliver greater value to their customers and gain a distinct sites in competition with other companies in the market at the local and international levels. Every company seeks to focus on one or more of the competitive capabilities in order to turn it into an obvious advantage or a number of competitive advantages to contribute in improving the performance and superiority over its competitors. Therefore, the management of companies no longer need only useful information for the internal aspects of the environment, but also need to include the external environment that includes various and constantly changin
... Show MoreEstablishing the systemic character of vocabulary, its relationship with other language systems, their interdependence creates the possibility of a comprehensive scientific study and description of the lexical system of each language, as well as contrastive comparative studies of several languages, including their phraseological composition.
It is known that not all words-components of phraseological units are equivalent in their role in the formation of the semantic content of phraseological units. In this regard, it is necessary to introduce the concept of a lexical dominant. To this we include words, which are kind of centers around which the entire semantic complex of phraseological units, the entire set of its words-componen
... Show MoreIn vivo study was made for the coumpounds 3-(ocetyl Salicyloyl)-5,6-O-isoprpy lideneL-ascorbicocid,2,3-(acetyl Salicyloyl )-5,6-o- isopropylidene-L-ascorbic acid and 2,3,5,6(acetyl Salicyloyl )-L- ascorbic acid .And a measurement was mod for the concentration of the liberated aspirin in blood samples a fter (2,3,4,6,8,10) hours of the initial dose for the animal .The results showed that the highest concentration of aspirin was after four hours of giving the dose to the animal which is in accordance with pharmacokinetics studies
The current research deals with the dialectical relationship resulting from the conflict in the violent combination and construction of the living ( the actor)and the dead (the item) in the structure of the Sinography construction and the emergence of the theatrical play space , which can be summed up by the following question: what is the nature of the dialectical relationship between the living (the actor) and the dead( the item) in the Sinography creation, which limited the research in a central objective : to identify the controversy of the living (actor) and the dead (item) in the performance unit of the theatrical scene . The research, in its objective limits set forth in its methodological framework, analyzes this controversy in o
... Show MoreThis study aims to impact statement played by banking governance according to the decisions of the Basel Committee in achieving the strategic objectives of the banks, But order to achieve the this goal has been the adoption of two hypotheses in addition to the two main hypotheses as sub answered preliminary The study seeks to verify their health and two (no correlation relationship and impact between Banking governance and achieve strategic objectives), has been tested hypotheses. Study has reached
... Show MoreThis study describes preparation a new series of tetra-dentate N2O2 dinuclear complexes Cr(III), Co(II)and Cu(II) of the Schiff base 2-[5-(2-hydroxy-phenyl)-1,3,4-thiadiazol-2-ylimino]-methyl-naphthalen-1-ol], (LH2) derived from 1-hydroxy-naphthalene-2-carbaldehyde with 2-amino-5-(2-hydroxy-phenyl)-1,3,4-thiadiazole. These ligands were characterized by FT-IR, UV-Vis, Mass spectra, elemental analysis, and 1H-NMR. All prepared complexes have been characterized by conductance measurement, magnetic susceptibility, electronic spectra, infrared spectrum, thermal Analysis (TGA), and metal analysis by atomic absorption. The stoichiometry of metal to ligand, magnetic susceptibility, and electronic spectra measurements show an octahedral geom
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