The Local Stability of Solutions for a Nonlinear Equation by Haibo Yan, Ls Yong

“…The approach of Kruzkov’s device of doubling the variables is applied to establish the local stability of strong solutions for a nonlinear partial differential equation in the space L1(R) by assuming that the initial value only lies in the space L1(R)∩L∞(R).…”
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Approximate Solutions of Delay Parabolic Equations with the Dirichlet Condition by Deniz Agirseven

“…Finite difference and homotopy analysis methods are used for the approximate solution of the initial-boundary value problem for the delay parabolic partial differential equation with the Dirichlet condition. The convergence estimates for the solution of first and second orders of difference schemes in Hölder norms are obtained. …”
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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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Positive Solutions for the Initial Value Problem of Fractional Evolution Equations by He Yang, Yue Liang

“…As an example, we study the partial differential equation of the parabolic type of fractional order.…”
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Uniqueness and radial symmetry for an inverse elliptic equation by B. Emamizadeh, M. H. Mehrabi

“…We consider an inverse rearrangement semilinear partial differential equation in a 2-dimensional ball and show that it has a unique maximizing energy solution. …”
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An Analytic Solution for a Vasicek Interest Rate Convertible Bond Model by A. S. Deakin, Matt Davison

“…This paper provides the analytic solution to the partial differential equation for the value of a convertible bond. …”
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A New Proof of Central Limit Theorem for i.i.d. Random Variables by Zhaojun Zong, Feng Hu

“…Our main tool is the viscosity solution theory of partial differential equation (PDE).…”
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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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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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Nonlinear elliptic problems with the method of finite volumes by Sanjay Kumar Khattri

“…Numerically solving nonlinear partial differential equations consists of discretizing the nonlinear partial differential equation and then solving the formed nonlinear system of equations. …”
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Integral price formulas for lookback options by Chenglong Xu, Yue Kuen Kwok

“…The intricacies in the derivation procedures using the partial differential equation techniques stem from the degenerate nature of the pricing models, where the lookback state variables appear only in the auxiliary conditions but not in the governing differential equations. …”
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Application of Asymptotic Analysis of a High-Dimensional HJB Equation to Portfolio Optimization by Lei Hu

“…The Hamilton–Jacobi–Bellman equation formulated from the optimal investment problem is a high-dimensional nonlinear partial differential equation and difficult to find its analytical or numerical solutions. …”
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A Generalized Nonlinear Gronwall-Bellman Inequality with Maxima in Two Variables by Yong Yan

“…We apply our result to a boundary value problem of a partial differential equation with maxima for uniqueness.…”
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Qualitative Analysis of Coating Flows on a Rotating Horizontal Cylinder by Marina Chugunova, Roman M. Taranets

“…We consider a nonlinear 4th-order degenerate parabolic partial differential equation that arises in modelling the dynamics of an incompressible thin liquid film on the outer surface of a rotating horizontal cylinder in the presence of gravity. …”
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New Exact Solutions of Burgers’ Equation Using Power Index Method by Khalil Ahmad, Khudija Bibi

“…In this method, we choose suitable indexes of independent variables and similarity transformation so that the partial differential equation may be converted into ODE. We have obtained analytic solution of the ODE by using symbolic package Maple. …”
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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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Exact Solutions of the Space Time Fractional Symmetric Regularized Long Wave Equation Using Different Methods by Özkan Güner, Dursun Eser

“…We apply the functional variable method, exp-function method, and (G′/G)-expansion method to establish the exact solutions of the nonlinear fractional partial differential equation (NLFPDE) in the sense of the modified Riemann-Liouville derivative. …”
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Finite Volume Element Approximation for the Elliptic Equation with Distributed Control by Quanxiang Wang, Tengjin Zhao, Zhiyue Zhang

“…In this paper, we consider a priori error estimates for the finite volume element schemes of optimal control problems, which are governed by linear elliptic partial differential equation. The variational discretization approach is used to deal with the control. …”
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Basic Properties of Incomplete Macdonald Function with Applications by Jian-Jun Shu, Kunal Krishnaraj Shastri

“…This paper also shows that the incomplete Macdonald function, as a simple closed-form expression, is a particular solution to a parabolic partial differential equation, which arises naturally in a wide variety of transient and diffusion-related phenomena.…”
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The Rayleigh quotient and dynamic programming by Richard Bellman

“…The purpose of this paper is to derive a nonlinear partial differential equation for which λ given by (1.3), is one value of the solution. …”
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