We study the stability of a unique weak solution to certain parabolic systems with nonstandard growth condition, which are additionally dependent on a cross-diffusion term. More precisely, we show that two unique weak solutions of the considered syst...
In this paper, we study weak solutions to the following nonlinear parabolic partial differential equation
In this paper, we show the application of the meshless numerical method called “Generalized Finite Diference Method” (GFDM) for solving a model for tumor growth with nutrient density, extracellular matrix and matrix degrading enzymes, [recently propo...
In this paper, exact solutions of semilinear equations having exponential growth in the space variable x are found. Semilinear Schrödinger equation with logarithmic nonlinearity and third-order evolution equations arising in optics with logarith...
Microalgae can be a future source of biomass with a wide range of applications, including its use to solve current environmental issues. One of the main variables for microalgal cultivation is the light supply: (i) its intensity that often does not p...
The high-temperature oxidation behaviors of polycrystalline Co-30Ni-10Al-4W-4Ti-2Ta superalloys with Cr contents ranging from 1 to 5 at.% are characterized at 900 °C to provide benchmark data for the alloy design of the CoNi-based superalloys. Th...
A generalisation of the Lie symmetry method is applied to classify a coupled system of reaction-diffusion equations wherein the nonlinearities involve arbitrary functions in the limit case in which one equation of the pair is quasi-steady but the oth...
We employed the selective-area-epitaxy technique using metalorganic chemical vapor deposition to fabricate and study samples of semiconductor heterostructures that incorporate highly strained InGaAs quantum wells (980–990 nm emission wavelength...
In this article, the parabolic dense fuzzy set is defined, and its basic arithmetic operations are studied with graphical illustration. The lock set concept is incorporated in a parabolic dense fuzzy set. Then, it is applied to the problems of fisher...
A mathematical model able to simulate the physical, chemical and biological interactions prevailing in multispecies biofilms in the presence of a toxic heavy metal is presented. The free boundary value problem related to biofilm growth and evolution...
The energy requirements for conditioning spaces have been increasing primarily due to population growth and climate change. This paper shows a comparison between an adsorption (ADC) and absorption cooling (ABC) systems to keep a building below the 25...
Highlights: European beech (Fagus sylvatica L.) and silver fir (Abies alba Mill.) displayed parabolic elevational trends of the cessation of xylem cell differentiation phases. Xylem phenology and growth rates of Scots pine (Pinus sylvestris L.) appea...
Continuous monitoring of vineyard dynamics is essential for optimizing viticultural practices and assessing plant health. While the seasonal behaviors of satellite-derived vegetation indices are widely studied, robust parametric modeling of these tem...
The combined damage induced by the nitrate molten salt corrosion and cyclic loading at elevated temperatures is an important damage issue for the reliable operation of concentrated solar power (CSP) plants. In previous works, the effect of the molten...
Cr2O3 scale growth and volatilization are the main cause of the performance degradation of solid oxide fuel cells (SOFCs) with an Fe-based ferritic stainless steel (FSS) interconnect. In this work, an amorphous Ti(Nb)-Si-C coating is prepared on the...
To investigate the growth kinetics of the reaction layer and mechanical strength of joined materials, we joined beryllium and reduced-activation ferritic–martensitic steel (F82H) by plasma sintering under various conditions and characterized the join...
The nucleation of cubic boron nitride (cBN) single crystals synthesized with lithium nitride (Li3N) as a catalyst under high pressure and high temperature (HPHT) was analyzed. Many nanometer-sized cubic boron nitride nuclei formed in the near surface...
A theory for crystal nucleation and growth with the recalescence front is developed. The theory is based on the saddle-point technique for evaluating a Laplace-type integral as well as the small parameter method for solving the moving boundary heat t...
In the theory of analytic and univalent functions, coefficients of functions’ Taylor series representation and their related functional inequalities are of major interest and how they estimate functions’ growth in their specified domains....
The fungal toxin fusicoccin (FC) induces rapid cell elongation, proton extrusion and plasma membrane hyperpolarization in maize coleoptile cells. Here, these three parameters were simultaneously measured using non-abraded and non-peeled segments with...
In this paper, a novel process is developed to cogenerate 4741 kg/h of methanol, 297.7 kW of electricity, and 35.73 ton/h of hot water, including a hydrogen purification system, an absorption–compression refrigeration cycle (ACRC), a regenerati...
Crack-growth behavior in yttria-stabilized zirconia-based thermal barrier coatings (TBCs) is investigated through a cyclic thermal fatigue (CTF) test to understand TBCs’ failure mechanisms. Initial cracks were introduced on the coatings’...
High-temperature surface oxidation kinetics were determined for low-carbon steel using a Joule heating device on hollow cylindrical specimens. The growth of the oxide layer was measured in situ between 800 and 1050
The grain growth behavior in a typical Ni-based superalloy was investigated using isothermal heat treatment experiments over a holding temperature range of 1353–1473 K. The experimental results showed that the grain structure continuously coarsened a...
Foreign trade in subdeveloped regions may lead to serious environmental problems. The direct and possible indirect ways in which foreign trade correlates with green economic efficiency in subdeveloped regions are qualitatively analyzed. Empirical tes...
The understanding of the oxidation behaviors of as-cast and annealed high-entropy alloys (HEAs) is currently limited. This work systematically investigates the influence of annealing on the microstructures and oxidation behaviors of AlCoCrFeNi-based...
With the growing scarcity of surface space, underground development has become essential for expanding human living space. Among various tunneling methods, pipe jacking stands out due to its economic advantages and minimal environmental impact. Recen...
2 October 2025
Stability theory offers a practical method on parametric studies that encompass scales in the boundary layer typically not captured in Large Eddy (LES) or Reynolds-Averaged Navier–Stokes (RANS) simulations. We investigated the transition modes...
A numerical simulation method is proposed to investigate the nonlinear growth of thermally grown oxide (TGO) on a novel coated steam dual-pipe system operating at 700 °C. Utilizing oxidation kinetics data from high-temperature water vapor experim...
This work presents an oxidation model that integrates high-temperature steel oxidation kinetics with CFD simulations to predict oxide scale formation during steel reheating under varying combustion atmospheres in the temperature range of 800–12...
In this paper, we derive the boundary integral equation (BIE), a single integrodifferential equation governing the evolutionary behavior of the interface function, paying special attention to the nonlinear liquidus equation and atomic kinetics. As a...
In this work, we study a bone remodeling model used to reproduce the phenomenon of osseointegration around endosseous implants. The biological problem is written in terms of the densities of platelets, osteogenic cells, and osteoblasts and the concen...
We consider a system of two differential equations modeling chemotaxis. The system consists of a parabolic equation describing the behavior of a biological species “u” coupled to an ODE patterning the concentration of a chemical substance...
The paper considers a new approach to modeling the relationship between the increase in woody phytomass in the pine forest and satellite-derived Normalized Difference Vegetation Index (NDVI) and Land Surface Temperature (LST) (MODIS/AQUA) data. The d...
This article examines contacting by means of ultrasonic welding between a cast aluminum winding and a copper conductor of a wheel hub drive for a passenger car. The effect of thermal stress on the formation and growth of intermetallic phases (IMC) in...
The performance of Cu-Fe alloy is related to the solidification structure, which is directly determined by the microstructure evolution during solidification. The solidification sequence, solid–liquid interface variation, and microstructural ev...
This study investigated the interfacial reactions between n-type Bi2(Te,Se)3 thermoelectric material, characterized by a highly-oriented (110) plane, and pure Sn and Sn-3.0Ag-0.5Cu (wt.%) solders, respectively. At 250 °C, the liquid-state Sn/Bi2(...
Thermal barrier coating (TBC) is a critical material in the aerospace domain to increase the lifetime of gas turbine components subjected to thermal load. The properties of TBC are strongly related to the growth of thermally grown oxide (TGO) whose m...
In this paper, we review the Fourier-spectral method for some phase-field models: Allen–Cahn (AC), Cahn–Hilliard (CH), Swift–Hohenberg (SH), phase-field crystal (PFC), and molecular beam epitaxy (MBE) growth. These equations are ver...
Recent decades have witnessed the emergence of interesting models of fractional partial differential equations. In the current work, a class of parabolic equations with regularized Hyper-Bessel derivative and the exponential source is investigated. M...
The effect of gallium on the oxide film structure and overall oxidation resistance of low melting point Sn–Bi–Zn alloys was investigated under air atmosphere using thermogravimetric analyses. The liquid alloys studied had a Ga content of...
High-temperature oxidation phenomena play a crucial role in steel production and processing. The development of new alloying concepts, the modification of production routes due to the decarbonization of steelmaking, and increasing quality demands wil...
Fe-Al intermetallic coatings were fabricated on 0Cr21Al6Nb stainless steel by pack cementation to systematically investigate the effects of temperature (650–800 °C) and holding time (2–16 h) on the coating microstructure, phase consti...
Carburization of cladding materials has long been a concern for the nuclear industry and has led to the restricted use of high-thermal conductivity fuels such as uranium carbides. With the rise of small modular reactors (SMRs) that frequently impleme...
In the present work, two mathematical diffusion models have been used to estimate the growth of the iron monoboride and diiron boride coating formed on AISI 420 steel. The boronizing of the steel was carried out with the solid diffusion packing metho...
This study proposes a mathematical modeling approach for the physical capital diffusion through the borders of countries. Physical capital is considered a crucial variable for the economic growth of a nation. Here, we use an extension of the economic...
An eight-week experiment was conducted to investigate the effects of temperature (20, 25, 30, and 35 °C) on growth performance, feed intake, energy metabolism, antioxidant capacity, and the stress response of juvenile Scylla paramamosain in a rec...
Light conditions and nitrogen fertilizer are crucial for plant growth, especially in the underground situations without sunlight and nitrogen deposition. In this paper, the effects of photoperiod (12 h and 16 h lighting time per day), light intensity...
Tool steel TD salt-bath vanadizing generally relies on expensive analytical-grade raw materials, yet systematic investigations into low-cost industrial borax-based vanadizing of 9SiCr steel remain insufficient. This work intends to optimize the indus...
The degradation process of HVOF-MCrAlY + APS-nanostructured YSZ (APS-nYSZ) thermal barrier coatings, produced using gas turbine OEM-approved MCrAlY powders, is investigated by studying the TGO growth and crack propagation behaviors in a thermal cycli...
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