Effects of Thermal Radiation on Mixed Convection Flow of a Micropolar Fluid from an Unsteady Stretching Surface with Viscous Dissipation and Heat Generation/Absorption by Khilap Singh, Manoj Kumar

“…The model contains nonlinear coupled partial differential equations which have been converted into ordinary differential equation by using the similarity transformations. …”
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SEMI-ANALYTUCAL SOLUTION TO DYNAMIC ANALYSIS FOR PLOUGH SYSTEM by CHEN Hong Yue, ZHANG Kun, ZHANG Yu, MAO Jun, SONG Qiu Shuang

“…Dynamic model of plough system including three partial differential equations were solved with separation variables method. …”
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Flow over Exponentially Stretching Sheet through Porous Medium with Heat Source/Sink by I. Swain, S. R. Mishra, H. B. Pattanayak

“…The governing nonlinear partial differential equations are transformed into a system of coupled nonlinear ordinary differential equations and then solved numerically using a fourth-order Runge-Kutta method with a shooting technique. …”
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Chemical Reaction Effect on Transient Free Convective Flow past an Infinite Moving Vertical Cylinder by Ashish Paul, Rudra Kanta Deka

“…The closed-form solutions of the dimensionless governing partial differential equations are obtained in terms of Bessel's functions and modified Bessel's functions by the Laplace transform technique. …”
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On viable therapy strategy for a mathematical spatial cancer model describing the dynamics of malignant and healthy cells by Alexander S. Bratus, Svetlana Yu. Kovalenko, Elena Fimmel

“…The mathematical model considered consists of three nonlinear parabolic partial differential equations which describe spatial dynamics of malignant cells as well as healthy ones, and of the concentration of the drug. …”
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Unsteady MHD Mixed Convection Flow of Chemically Reacting Micropolar Fluid between Porous Parallel Plates with Soret and Dufour Effects by Odelu Ojjela, N. Naresh Kumar

“…A suitable similarity transformation is used to reduce the governing partial differential equations into nonlinear ordinary differential equations and then solved numerically by the quasilinearization method. …”
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Solving arbitrary one-loop reduction via generating function by Tingfei Li, Yuekai Song, Liang Zhang

“…We first establish the partial differential equations governing the higher-pole generating function. …”
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Stagnation Point Flow of Nanofluid over a Moving Plate with Convective Boundary Condition and Magnetohydrodynamics by Fazle Mabood, Nopparat Pochai, Stanford Shateyi

“…The governing partial differential equations for the fluid flow, temperature, and concentration are reduced to a system of nonlinear ordinary differential equations. …”
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On the Regularity of the Entropy Solution of the Fractional-Semigeostrophic Equation Using Ultrafilters by Gilles Tamba Bokolo

“…This work lays the groundwork for future studies on fractional partial differential equations in geophysical contexts, potentially leading to more accurate predictive models in meteorology and oceanography.…”
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Modeling Multicellular Systems Using Subcellular Elements by T. J. Newman

“…We present here a detailed description of the model, and use successive mean-field approximations to connect it to more coarse-grained approaches, such as discrete cell-based algorithms and coupled partial differential equations. We also discuss efficient algorithms for encoding the model, and give an example of a simulation of an epithelial sheet. …”
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Some Nonlinear Fractional PDEs Involving β-Derivative by Using Rational exp−Ωη-Expansion Method by Haifa Bin Jebreen

“…In this article, some new nonlinear fractional partial differential equations (PDEs) (the space-time fractional order Boussinesq equation; the space-time (2 + 1)-dimensional breaking soliton equations; and the space-time fractional order SRLW equation) have been considered, in which the treatment of these equations in the diverse applications are described. …”
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Identification of the boundary regime in the process of water-oil displacement from the reservoir by Gamzaev Khanlar

“…The water-oil displacement process (from a rectangular reservoir) has been considered, that is described by a nonlinear system of partial differential equations with respect to the reservoir pressure (RP) and displacing phase saturation (DPS). …”
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Application of Local Fractional Homotopy Perturbation Method in Physical Problems by Nabard Habibi, Zohre Nouri

“…Most physical phenomena are modeled according to partial differential equations. It is difficult for nonlinear models to obtain the closed form of the solution, and in many cases, only an approximation of the real solution can be obtained. …”
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Recent Developments on Operator-Difference Schemes for Solving Nonlocal BVPs for the Wave Equation by Mehmet Emir Koksal

“…Two new second-order difference schemes recently appeared in the literature are compared numerically with each other and with the rather old first-order difference scheme all to solve abstract Cauchy problem for hyperbolic partial differential equations with time-dependent unbounded operator coefficient. …”
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Nonlinear iterative approximation of steady incompressible chemically reacting flows by Gazca-Orozco, Pablo Alexei, Heid, Pascal, Süli, Endre

“…We consider a system of nonlinear partial differential equations modelling steady flow of an incompressible chemically reacting non-Newtonian fluid, whose viscosity depends on both the shear-rate and the concentration; in particular, the viscosity is of power-law type, with a power-law index that depends on the concentration. …”
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Simulating Smoke Filling in Big Halls by Computational Fluid Dynamics by W. K. Chow, C. L. Chow, S. S. Li

“…Mathematical aspects concerning of discretization of partial differential equations and algorithms for solving the velocity-pressure linked equations are briefly outlined. …”
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A toxin-mediated size-structured population model: Finite difference approximation and well-posedness by Qihua Huang, Hao Wang

“…Motivated by the fact that individuals with different sizes may have different sensitivities to toxins, we develop a toxin-mediated size-structured model which is given by a system of first order fully nonlinear partial differential equations (PDEs). It is very possible that this work represents the first derivation of a PDE model in the area of ecotoxicology. …”
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Finite element approximation of a population spatial adaptation model by Gonzalo Galiano, Julián Velasco

“…In [18], Sighesada, Kawasaki and Teramoto presented a system of partial differential equations for modeling spatial segregation of interacting species. …”
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PDE Modeling of a Microfluidic Thermal Process for Genetic Analysis Application by Reza Banaei Khosroushahi, Horacio J. Marquez, Jose Martinez-Quijada, Christopher J. Backhouse

“…The general partial differential equations describing the dynamics of the system are separated into steady-state and transient parts which are derived for a carefully chosen three-dimensional axisymmetric model. …”
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On the Fractional View Analysis of Keller–Segel Equations with Sensitivity Functions by Haobin Liu, Hassan Khan, Rasool Shah, A. A. Alderremy, Shaban Aly, Dumitru Baleanu

“…The suggested procedure is very attractive and straight forward and therefore can be modified to solve high nonlinear fractional partial differential equations and their systems.…”
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