Cauchy-Dirichlet problem for the nonlinear degenerate parabolic equations by Ismail Kombe

“…We will investigate the nonexistence of positive solutions for the following nonlinear parabolic partial differential equation: ∂u/∂t=ℒu+V(w)up−1 in Ω×(0,T), 1<p<2, u(w,0)=u0(w)≥0 in Ω, u(w,t)=0 on ∂Ω×(0,T) where ℒ is the subelliptic p-Laplacian and V∈Lloc1(Ω).…”
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Dynamical investigation of a supported pipe line section with flowing liquid when intermidiate support is removed by Rimantas Didžgalvis, Antanas Sudintas

“…Such a mechanical system was described by as the analytical model — the system of differential equation and the solutions were given. Finally, those solutions, could be used for the finding of normal tensions in the walls of the pipes. …”
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Solutions and Conservation Laws of a (2+1)-Dimensional Boussinesq Equation by Letlhogonolo Daddy Moleleki, Chaudry Masood Khalique

“…We study a nonlinear evolution partial differential equation, namely, the (2+1)-dimensional Boussinesq equation. …”
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INHERENT CHARACTERISTICS ANALYSIS OF GRAPHENE REINFORCED CONICAL SHELLS WITH ARBITRARY BOUNDARY CONDITIONS by JIA WeiGe

“…The mechanics model for graphene reinforced composites and the free vibration differential equation of graphene reinforced conical shells were deduced. …”
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Pricing Parisian Option under a Stochastic Volatility Model by Min-Ku Lee, Kyu-Hwan Jang

“…A stochastic volatility correction to the Black-Scholes price of the Parisian option is obtained in a partial differential equation form and the solution is characterized numerically.…”
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Controllability in Hybrid Kinetic Equations Modeling Nonequilibrium Multicellular Systems by Carlo Bianca

“…Specifically, the analysis shows that the moments are solution of a Riccati-type differential equation.…”
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Existence and uniqueness theorems for some fourth-order nonlinear boundary value problems by Ruyun Ma

“…This paper is concerned with the problems of existence and uniqueness of solutions for the nonlinear fourth-order ordinary differential equation y′′′′+λy′′+ky+G(x,y,y′,y′′,y′′′)=f(x,y,y′,y′′,y′′′) with one of a particular set of boundary conditions.…”
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On nth-order differential operators with Bohr-Neugebauer type property by Aribindi Satyanarayan Rao

“…If the differential operator dndtn−B has a Bohr-Neugebauer type property for Bochner almost periodic functions, then, for any Stepanov almost periodic continuous function g(t) and any Stepanov-bounded solution of the differential equation dndtnu(t)−Bu(t)=g(t), u(n−1),…,u′,u are all almost periodic.…”
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A Numerical Method for Computing the Principal Square Root of a Matrix by F. Soleymani, S. Shateyi, F. Khaksar Haghani

“…Finally, application of the presented approach is illustrated in solving a matrix differential equation.…”
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The Pricing of Vulnerable Options in a Fractional Brownian Motion Environment by Chao Wang, Shengwu Zhou, Jingyuan Yang

“…Under the assumption of the stock price, interest rate, and default intensity obeying the stochastic differential equation driven by fractional Brownian motion, the jump-diffusion model is established for the financial market in fractional Brownian motion setting. …”
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Stability of a Three-Species Cooperative System with Time Delays and Stochastic Perturbations by Jinxing Zhao, Yuanfu Shao

“…We establish the sufficient criteria of the asymptotical stability and stability in probability by constructing a neutral stochastic differential equation and some suitable functionals. The impacts of time delays and stochastic perturbations to the system dynamics are revealed by some numerical simulations at the end.…”
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On a Fractional SPDE Driven by Fractional Noise and a Pure Jump Lévy Noise in ℝd by Xichao Sun, Zhi Wang, Jing Cui

“…We study a stochastic partial differential equation in the whole space x∈ℝd, with arbitrary dimension d≥1, driven by fractional noise and a pure jump Lévy space-time white noise. …”
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Nematic Liquid Crystal Locking Menisci by Milan Svetec, Mitja Slavinec

“…The resulting Euler-Lagrange differential equation is solved numerically. We determine conditions for the defects to be trapped by the meniscus.…”
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Permanence, Extinction, and Almost Periodic Solution of a Nicholson's Blowflies Model with Feedback Control and Time Delay by Haihui Wu, Shengbin Yu

“…By applying the comparison theorem of the differential equation and fluctuation lemma and constructing a suitable Lyapunov functional, sufficient conditions which guarantee the permanence, extinction, and existence of a unique globally attractive positive almost periodic solution of the system are obtained. …”
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Study of Time Evolution for Approximation of Two-Body Spinless Salpeter Equation in Presence of Time-Dependent Interaction by Hadi Sobhani, Hassan Hassanabadi

“…We use the Lewis-Riesenfeld dynamical invariant method and series solution to obtain the solutions of the differential equation. We have also done some calculations in order to derive the time evolution operator for the considered problem.…”
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Spectral Differentiation and Mimetic Methods for Solving the Scalar Burger’s Equation by Bertha K. Rodriguez-Chavez, Yessica E. Zarate-Pedrera

“…In the present work, the spectral differentiation method was studied to solve the scalar Burger’s partial differential equation. This equation has been of considerable physical interest as it can be regarded as a simplified version of the Navier-Stokes equations. …”
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Machine learning to identify environmental drivers of phytoplankton blooms in the Southern Baltic Sea by Maximilian Berthold, Pascal Nieters, Rahel Vortmeyer-Kley

“…We employed generalized additive mixed models to characterize similar blooming patterns and trained an artificial neural network within the Universal Differential Equation framework to learn a differential equation representation of these pattern. …”
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A relationship between the modified Euler method and e by Richard B. Darst, Thomas P. Dence

“…Approximating solutions to the differential equation dy/dx=f(x,y) where f(x,y)=y by a generalization of the modified Euler method yields a sequence of approximates that converge to e. …”
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New Applications of a Kind of Infinitesimal-Operator Lie Algebra by Honwah Tam, Yufeng Zhang, Xiangzhi Zhang

“…Applying some reduced Lie algebras of Lie symmetry operators of a Lie transformation group, we obtain an invariant of a second-order differential equation which can be generated by a Euler-Lagrange formulism. …”
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Further studies of fully developed flow through ducts of arbitrary section by the contour line-conformal mapping technique by J. Mazumdar, D. Hopkins

“…The amplitude of the oscillatory velocity is then obtained from an ordinary integro-differential equation. Several examples of a practical nature are given, with some that have not yet been discussed in the literature. …”
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