Results 31 to 40 of about 35,012 (233)
On an inverse problem for a nonlinear third order in time partial differential equation
Results in Applied Mathematics, 2022 In this article, first we convert an inverse problem of determining the unknown timewise terms of nonlinear third order in time partial differential equation (PDE) from knowledge of two boundary measurements to the auxiliary system of integral equations.
M.J. Huntul, I. Tekin
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The General Fractional Derivative and Related Fractional Differential Equations
Mathematics, 2020 In this survey paper, we start with a discussion of the general fractional derivative (GFD) introduced by A. Kochubei in his recent publications. In particular, a connection of this derivative to the corresponding fractional integral and the Sonine ...
Yuri Luchko, Masahiro Yamamoto
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International Journal of Mathematics and Mathematical Sciences, 2014 Singular nonlinear initial-value problems (IVPs) in first-order and second-order partial differential equations (PDEs) arising in fluid mechanics are semianalytically solved. To achieve this, the modified decomposition method (MDM) is used in conjunction
Nemat Dalir
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Entropy, 2023 Physics-informed neural networks (PINNs) are effective for solving partial differential equations (PDEs). This method of embedding partial differential equations and their initial boundary conditions into the loss functions of neural networks has ...
Kuo Sun, Xinlong Feng
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Enforcing local non-zero constraints in PDEs and applications to hybrid imaging problems [PDF]
, 2015 We study the boundary control of solutions of the Helmholtz and Maxwell equations to enforce local non-zero constraints. These constraints may represent the local absence of nodal or critical points, or that certain functionals depending on the solutions
Alberti, Giovanni S.
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Consensus ADMM for Inverse Problems Governed by Multiple PDE Models
, 2021 The Alternating Direction Method of Multipliers (ADMM) provides a natural way of solving inverse problems with multiple partial differential equations (PDE) forward models and nonsmooth regularization. ADMM allows splitting these large-scale inverse problems into smaller, simpler sub-problems, for which computationally efficient solvers are available ...
Lozenski, Luke, Villa, Umberto
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International Transactions on Electrical Energy Systems, 2023 In this paper, the development and application of the radial basis function-finite difference (RBF-FD) method and the RBF-finite difference time domain (RBF-FDTD) method for solving electrical transient problems in power systems that are defined by the ...
Duc-Quang Vu +2 more
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Accelerated Variational PDEs for Efficient Solution of Regularized Inversion Problems
Journal of Mathematical Imaging and Vision, 2019 We further develop a new framework, called PDE acceleration, by applying it to calculus of variation problems defined for general functions on ℝ n , obtaining efficient numerical algorithms to solve the resulting class of optimization problems based on simple discretizations of their corresponding accelerated PDEs. While the resulting family of PDEs
Benyamin, Minas +3 more
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, 2020 In this paper, we establish a novel unique continuation property for two-dimensional anisotropic elasticity systems with partial information. More precisely, given a homogeneous elasticity system in a domain, we investigate the unique continuation by ...
Cheng, Jin +3 more
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Gradient Statistics-Based Multi-Objective Optimization in Physics-Informed Neural Networks
Sensors, 2023 Modeling and simulation of complex non-linear systems are essential in physics, engineering, and signal processing. Neural networks are widely regarded for such tasks due to their ability to learn complex representations from data.
Sai Karthikeya Vemuri, Joachim Denzler
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