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, the series solution is applied to solve third order fuzzy differential equations with a fuzzy initial value. The proposed method applies Taylor expansion in solving the system and the approximate solution of the problem which is calculated in the form of a rapid convergent series; some definitions and theorems are reviewed as a basis in solving fuzzy differential equations. An example is applied to illustrate the proposed technical accuracy. Also, a comparison between the obtained results is made, in addition to the application of the crisp solution, when theï€ ï¡-level equals one.
In this paper, the author established some new integral conditions for the oscillation of all solutions of nonlinear first order neutral delay differential equations. Examples are inserted to illustrate the results.
This paper is concerned with the oscillation of all solutions of the n-th order delay differential equation . The necessary and sufficient conditions for oscillatory solutions are obtained and other conditions for nonoscillatory solution to converge to zero are established.
Drag has long been identified as the main reason for the loss of energy in fluid transmission like pipelines and other similar transportation channels. The main contributor to this drag is the viscosity as well as friction against the pipe walls, which will results in more pumping power consumption.
The aim in this study was first to understand the role of additives in the viscosity reduction and secondly to evaluate the drag reduction efficiency when blending with different solvents.
This research investigated flow increase (%FI) in heavy oil at different flow rates (2 to 10 m3/hr) in two pipes (0.0381 m & 0.0508 m) ID By using different additives (toluene and naphtha) with different concent
... Show MoreIn this paper, we propose new types of non-convex functions called strongly --vex functions and semi strongly --vex functions. We study some properties of these proposed functions. As an application of these functions in optimization problems, we discuss some optimality properties of the generalized nonlinear optimization problem for which we use, as an objective function, strongly --vex function and semi strongly --vex function.
Summary First: The importance of the study and the need for it: The society is composed of an integrated unit of groups and institutions that seek to achieve a specific goal within a system of salary, and the family remains the most influential institutions on the individual and the unity of society, with the roles and responsibilities of the individual and society, and through the continuation and strength of other social organizations derive their ability On the other hand, any break-up in the institution of the family is reflected negatively on the cohesion of society and its interdependence, and the causes of this disintegration vary from society to another, but family problems remain the main factor in obtaining it. Second: Study Ob
... Show MoreCalciturbidites are similar to siliciclastic turbidites in structure, texture, basin physiography and processes of deposition; nevertheless, their clasts (grains) are carbonate minerals. Turbidity currents transport carbonate grains from carbonate source areas and coastal areas to the deep basins after passing the shelf (peri-platform). These currents are triggered by short-lived catastrophic events, such as tsunamis, earthquakes, marine slides, and typhoons. The Late Cretaceous Zagros Foreland and Hinterland in NE-Iraq (Kurdistan Region) was an active source for the shedding of voluminous sediments to the deep basin of Zagros Foreland Basin. During late Campanian, Shiranish Formation was deposited in the foreland basin; it occurs in the
... Show MoreA fast moving infrared excess source (G2) which is widely interpreted as a core-less gas and dust cloud approaches Sagittarius A* (Sgr A*) on a presumably elliptical orbit. VLT
The study area is encompassed by the 33.59-34.93°N latitudes and 45.44-46.39°E longitudes and divided into four groups with respect to earthquake event locations. We determined fault plane solutions, moment magnitudes, focal depths, and trend of slip with the direction of the moment stress axes (P, N, and T) for 102 earthquakes. These earthquakes had a local magnitude in the range between 4.0 and 6.4 for the time period from January 2018 to the end of August 2019, with focal depths ranged between 6 and 17 km. Waveform moment tensor inversion technique was used to analyze the database constructed from seismic stations on local and neighboring country networks (Iraq, Iran, and Turkey). We separated the studie
... Show MoreDetecting protein complexes in protein-protein interaction (PPI) networks is a challenging problem in computational biology. To uncover a PPI network into a complex structure, different meta-heuristic algorithms have been proposed in the literature. Unfortunately, many of such methods, including evolutionary algorithms (EAs), are based solely on the topological information of the network rather than on biological information. Despite the effectiveness of EAs over heuristic methods, more inherent biological properties of proteins are rarely investigated and exploited in these approaches. In this paper, we proposed an EA with a new mutation operator for complex detection problems. The proposed mutation operator is formulated und
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