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.
Maintaining the quality of apricot fruits during storage is not an easy task due to the changes in their physical and chemical properties, so it is necessary to use less expensive, easy to apply, environmentally friendly, and safer preservatives to maintain the nutritional value of apricot. The damage to some fruits during storage can be a source of infection, which leads to the damage of healthy fruits more quickly, which requires building an intelligent model to detect damaged fruits. The aim of the research is to study the effect of immersing apricots in lemon juice once and sugar-water solution again on the quality properties of apricots, including sweetness, color, hardness, and water content. On the other hand, the YOLOv7 algorithm wa
... Show MoreThe study aimed to : - To determine whether there are significant differences between Fartlek training and the increase in the molecular biology (VEGF - basal fibroblast growth factor) for arena and field players in an (800m) youth event. - Determine whether there are statistically significant differences between Fartlek training and the increase in molecular biology and some physical variables for the players (800m) in the arena and field for youth. - Determine whether the Fartlek training method is the most appropriate to achieve statistically significant differences in the research variables for the players (800m) in the arena and field for youth. The researchers used the experimental method for its suitability and the nature of the rese
... Show MoreThe research aims to identify: 1-Designing a test to measure the movement compatibility of the eye and the leg for the students of the Faculty of Physical Education and Sports Sciences, Samarra University. 2-Codification (setting scores and standard levels) for the results of the motor compatibility test for the eye and the leg for students of the Faculty of Physical Education and Sports Sciences, Samarra University. The researchers reached the some following conclusions: 1-A test to measure the movement compatibility of the eye and the leg for the students of the Faculty of Physical Education and Sports Sciences. 2-There is a discrepancy in the standard levels of the research sample.
The operating characteristics of optoelectronic devices depend critically on the properties physical of the constituent materials, interesting compound has been focused on this research formed from group III and V of the periodic table. Thin film n-InSb heterjuntion were successfully fabricated on p-Si substrates by thermal evaporation technique at different annealing temperature (as prepared, 400,500,600) °C. The effect of annealing temperature on the structural, surface morphology, optical and optoelectronic properties of InSb films were investigated and studied. The crystal structure of the film was characterized by X-ray diffraction and techniques. AFM techniques inspect the surface morphology of InSb films, the study presented the val
... Show MoreParental socialization trends impacting seriously on the growth of individual
personality and psychological health trends ,love, acceptance and on confidence help
children to grow as a person who loves other accept others and trust and negative parental
attitudes such as excess portents us or negligence . and the focusing and demonstrate a
negative impact on the growth of excess an mental health and family play a significant role in
a childes life we can see how many manifestation of compatibility or incompatibility thatappear on individual behaviors and achieve their success or failure in life be returned to the
of human relations that prevailed between the family members of children in various stages of
his life fi