Traveling Wave Optical Solutions for the Generalized Fractional Kundu–Mukherjee–Naskar (gFKMN) Model
Mathematics, 2023 The work considers traveling wave optical solutions for the nonlinear generalized fractional KMN equation. This equation is considered for describing pulse propagation in optical fibers and communication systems using two quite similar approaches, based ...
Yong Tang
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Differential games and nonlinear first order PDE on bounded domains
Manuscripta Mathematica, 1984 This paper studies the fully nonlinear first order partial differential equation \(u+H(x,Du)=0\) in a bounded domain \(\theta\) with \(u=g\) on the boundary of \(\theta\) using the connection between viscosity solutions and differential games or control theory. Here the control problem involves the exit time from the domain.
Evans, L.C., Ishii, H.
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Space-time numerical simulation and validation of analytical predictions for nonlinear forced dynamics of suspended cables [PDF]
, 2008 This paper presents space-time numerical simulation and validation of analytical predictions for the finite-amplitude forced dynamics of suspended cables.
Rega, Giuseppe, Srinil, Narakorn
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On microlocal analyticity of solutions of first-order nonlinear PDE [PDF]
Annales de l'Institut Fourier, 2009 We study the microlocal analyticity of solutions u of the nonlinear equationut=f(x,t,u,ux)where f(x,t,ζ 0 ,ζ) is complex-valued, real analytic in all its arguments and holomorphic in (ζ 0 ,ζ). We show that if the function u is a C 2 solution, σ∈CharL u and 1 iσ([L u ,L u ¯])<0 or if u is a C 3 solution, σ∈CharL u , σ([L u ,L u ¯])=0, and σ([L u
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Faber-Schauder Wavelet Sparse Grid Approach for Option Pricing with Transactions Cost
Abstract and Applied Analysis, 2014 Transforming the nonlinear Black-Scholes equation into the diffusion PDE by introducing the log transform of S and (T−t)→τ can provide the most stable platform within which option prices can be evaluated.
Shu-Li Mei
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Numerical solution of a malignant invasion model using some finite difference methods
Demonstratio Mathematica, 2023 In this article, one standard and four nonstandard finite difference methods are used to solve a cross-diffusion malignant invasion model. The model consists of a system of nonlinear coupled partial differential equations (PDEs) subject to specified ...
Appadu Appanah Rao +1 more
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Gevrey micro-regularity for solutions to first order nonlinear PDE
Journal of Differential Equations, 2009 In this interesting paper, the authors study the microlocal Gevrey regularity of \(C^2\) solutions to a first-order nonlinear PDE. More precisely, let \(f=f(x,t,\zeta_0,\zeta)\) be Gevrey of order \(s>1\) and holomorphic in the variables \((\zeta_0,\zeta)\). Consider a solution \(u\in C^2\) to \(u_t=f(x,t,u,u_x)\).
Barostichi, R.F., Petronilho, G.
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Are physiological oscillations physiological?
The Journal of Physiology, EarlyView., 2023 Abstract figure legend Mechanisms and functions of physiological oscillations. Abstract Despite widespread and striking examples of physiological oscillations, their functional role is often unclear. Even glycolysis, the paradigm example of oscillatory biochemistry, has seen questions about its oscillatory function.
Lingyun (Ivy) Xiong, Alan Garfinkel
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On the C ∞ Wave-Front Set of Solutions of First-Order Nonlinear PDE's [PDF]
Proceedings of the American Mathematical Society, 1995 Let Ω ⊂ R m + 1 \Omega \subset {{\mathbf {R}}^{m + 1}} be a neighborhood of the origin and assume u ∈ C 2
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Analysis and optimal boundary control of a nonstandard system of phase field equations [PDF]
, 2012 We investigate a nonstandard phase field model of Cahn-Hilliard type. The model describes two-species phase segregation and consists of a system of two highly nonlinearly coupled PDEs.
Colli, Pierluigi +2 more
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