Pulsation Calculation of Cylindrical Underwater Gas Explosion Products in Well by A. M. Sheiko, V. V. Ivashechkin, V. V. Veremenuk

“…The paper considers a mathematical model of pulsation process of cylindrical underwater gas explosion products in the well at gas-impulse regeneration filters. A differential equation of the second-order with constant coefficients has been derived. …”
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Bifurcations of Tumor-Immune Competition Systems with Delay by Ping Bi, Heying Xiao

“…A tumor-immune competition model with delay is considered, which consists of two-dimensional nonlinear differential equation. The conditions for the linear stability of the equilibria are obtained by analyzing the distribution of eigenvalues. …”
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Necessary and Sufficient Conditions of Optimality for a Damped Hyperbolic Equation in One-Space Dimension by Ismail Kucuk, Kenan Yildirim

“…The present paper deals with the necessary optimality condition for a class of distributed parameter systems in which the system is modeled in one-space dimension by a hyperbolic partial differential equation subject to the damping and mixed constraints on state and controls. …”
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Unified Treatment of a Class of Spherically Symmetric Potentials: Quasi-Exact Solution by H. Panahi, M. Baradaran

“…We illustrate that all models give rise to the same basic differential equation, which is expressible as an element of the universal enveloping algebra of sl(2). …”
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New Results on the Noise Figure of HEMTs by M. A. Grado Caffaro, M. Grado Caffaro

“…The fundamental relationship that gives minimum noise figure is derived from a first-order linear partial differential equation, which is established by assuming reasonable statements based on experience.…”
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The stability of collocation methods for VIDEs of second order by Edris Rawashdeh, Dave McDowell, Leela Rakesh

“…Simplest results presented here are the stability criteria of collocation methods for the second-order Volterra integro differential equation (VIDE) by polynomial spline functions. …”
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Analytical Solution to 1D Compressible Navier-Stokes Equations by Changsheng Dou, Zishu Zhao

“…We find an interesting phenomenon on the solution to 1D compressible isentropic Navier-Stokes equations with constant viscosity coefficient on x,t∈0,+∞×R+, that is, the solutions to the initial boundary value problem to 1D compressible Navier-Stokes equations in half space can be transformed to the solution to the Riccati differential equation under some suitable conditions.…”
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Image Texture Analysis and Edge Detection Algorithm Based on Anisotropic Diffusion Equation by Xiaoqin Li

“…This paper uses partial differential equation image processing techniques to establish image texture analysis models based on nonlinear anisotropic diffusion equations for image denoising, image segmentation, and image decomposition. …”
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Well-Testing Model for Dual-Porosity Reservoir considering Stress-Sensitivity and Elastic Outer Boundary Condition by Song Chol Kim, Song Guk Han, Yong Il Song, Jin Sim Kim, Myong Gun Hong

“…To solve this model, a nonlinear partial differential equation is changed into a linear form of a partial differential equation by introducing an effective well radius and applying Pedrosa’s transformation and perturbation transformation. …”
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Analytical Method in Solving Flow of Viscoelastic Fluid in a Porous Converging Channel by M. Esmaeilpour, Naeem Roshan, Negar Roshan, D. D. Ganji

“…An analytical method, called homotopy perturbation method (HPM), is used to compute an approximation to the solution of the nonlinear differential equation governing the problem of two-dimensional and steady flow of a second-grade fluid in a converging channel. …”
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Hydrodynamics of Underwater Gas Explosion in Half-Closed Chamber Situated in Well by V. V. Ivashechkin, V. V. Veremenuk

“…The paper considers a mathematical model for pulsation process of underwater gas explosion products in a half-close cylindrical rigid chamber during gas-impulse regeneration of filters. Second-order differential equation with constant coefficients has been derived. …”
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High-Frequency Electromagnetic Field Coupling to Small Antennae in a Rectangular Resonator by Sergey Tkachenko, Jürgen Nitsch, Moawia Al-Hamid

“…The integral-differential equation for the current of an electrically small antenna, inside a resonator, which is induced by given sources, is approximately solved by the so-called “Method of Small Antenna,” both for dipole and loop antennas. …”
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A Class of PDEs with Nonlinear Superposition Principles by Li Peng, Liu Keying, Pan Zuliang, Zhong Weizhou

“…In the end, some applications of the PDEs are explained, which shows that the result has very subtle relations with linearization of partial differential equation.…”
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A Stochastic Approach to Modeling Food Pattern by Komla Elom Adedje, Diakarya Barro

“…In this paper, we propose a fractional differential equation of order one-half, to model the evolution through time of the dynamics of accumulation and elimination of the contaminant in the human organism with a deficient immune system, during consecutive intakes of contaminated food. …”
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Dynamical Analysis of a Pest Management Model with Saturated Growth Rate and State Dependent Impulsive Effects by Wencai Zhao, Tongqian Zhang, Xinzhu Meng, Yang Yang

“…Secondly, by using geometry theory of impulsive differential equation, the existence and stability of periodic solution of the system are discussed. …”
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Double Periodic Wave Solutions of the (2 + 1)-Dimensional Sawada-Kotera Equation by Zhonglong Zhao, Yufeng Zhang, Tiecheng Xia

“…Based on a general Riemann theta function and Hirota’s bilinear forms, we devise a straightforward way to explicitly construct double periodic wave solution of (2+1)-dimensional nonlinear partial differential equation. The resulting theory is applied to the (2+1)-dimensional Sawada-Kotera equation, thereby yielding its double periodic wave solutions. …”
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Exponential Stability of Periodic Solutions for Inertial Type BAM Cohen-Grossberg Neural Networks by Chunfang Miao, Yunquan Ke

“…First, by properly choosing variable substitution, the system is transformed to first order differential equation. Second, some sufficient conditions that ensure the existence and exponential stability of periodic solutions for the system are obtained by constructing suitable Lyapunov functional and using differential mean value theorem and inequality technique. …”
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Comparison of Analytical Solution of DGLAP Equations for... by Neelakshi N. K. Borah, D. K. Choudhury, P. K. Sahariah

“…The DGLAP equation for the nonsinglet structure function F 2 N S ( x , t ) at LO is solved analytically at low x by converting it into a partial differential equation in two variables: Bjorken x and t    ( t = l n ( Q 2 / Λ 2 ) and then solved by two methods: Lagrange’s auxiliary method and the method of characteristics. …”
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Global attractor for the lattice dynamical system of a nonlinear Boussinesq equation by Ahmed Y. Abdallah

“…As far as we are aware, our result here is the first concerning the lattice dynamical system corresponding to a differential equation of second order in time variable and fourth order in spatial variable with nonlinearity involving the gradients.…”
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Large diffusivity finite-dimensional asymptotic behaviour of a semilinear wave equation by Robert Willie

“…In the linear case, we show in a given sense that the asymptotic behaviour of solutions verifies a second-order ordinary differential equation. In the semilinear case, under suitable dissipative assumptions on the nonlinear term, we prove the existence of a global attractor for fixed diffusion and that the limiting attractor for large diffusion is finite dimensional.…”
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