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.
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That studies assumes
In the past two decades, maritime transport traffic has increased, especially in the case of container flow. The BAP (Berth Allocation Problem) (BAP) is a main problem to optimize the port terminals. The current manuscript explains the DBAP problems in a typical arrangement that varies from the conventional separate design station, where each berth can simultaneously accommodate several ships when their entire length is less or equal to length. Be a pier, serve. This problem was then solved by crossing the Red Colobuses Monkey Optimization (RCM) with the Genetic Algorithm (GA). In conclusion, the comparison and the computational experiments are approached to demonstrate the effectiveness of the proposed method contrasted with other
... Show MoreHysterectomy is one of the most common gynecological operations done worldwide. Early diagnosis of the psychosexual effects of a hysterectomy and the fast application of appropriate treatment can prevent further worsening and persistence of symptoms, especially with respect to higher levels of anxiety, depression, lower self-esteem, and sexual impact after a hysterectomy. The aim of this study was to assess the psychological and sexual problems of women with hysterectomy. A descriptive study was carried out from March 1, 2023 to May 25, 2023 to determine the level of psychosexual problems experienced by women after hysterectomy. A purposive (non-probability) sample of 120 women who visited the outpatient clinic at Baghdad Teaching H
... Show MoreIn this paper, a compartmental differential epidemic model of COVID-19 pandemic transmission is constructed and analyzed that accounts for the effects of media coverage. The model can be categorized into eight distinct divisions: susceptible individuals, exposed individuals, quarantine class, infected individuals, isolated class, infectious material in the environment, media coverage, and recovered individuals. The qualitative analysis of the model indicates that the disease-free equilibrium point is asymptotically stable when the basic reproduction number R0 is less than one. Conversely, the endemic equilibrium is globally asymptotically stable when R0 is bigger than one. In addition, a sensitivity analysis is conducted to determine which
... Show MoreTuberculosis status as the second leading causes of significant morbidity and mortality from an infectious disease worldwide, after human immunodeficiency virus (HIV). Sample collection was conducted at the Institute of Chest and Respiratory Diseases/Baghdad Medical City in Baghdad. The collection interval was from August to October 2014, 629 suspected TB patients were examined during this period. The results revealed among total 629 specimens, 56 (8.9%) of the specimens were positive by direct examination and 573 (91.1%) negative specimens by smear microscopy. Fifty six DNA samples were extracted from positive ZN smears of sputum specimens and 40 samples from healthy persons (as control) were subjected to molecular diagnosis by real tim
... Show MoreThis article deals with the approximate algorithm for two dimensional multi-space fractional bioheat equations (M-SFBHE). The application of the collection method will be expanding for presenting a numerical technique for solving M-SFBHE based on “shifted Jacobi-Gauss-Labatto polynomials” (SJ-GL-Ps) in the matrix form. The Caputo formula has been utilized to approximate the fractional derivative and to demonstrate its usefulness and accuracy, the proposed methodology was applied in two examples. The numerical results revealed that the used approach is very effective and gives high accuracy and good convergence.