Exact Solutions of Reaction–Diffusion PDEs with Anisotropic Time Delay
Mathematics, 2023 This study is devoted to reaction–diffusion equations with spatially anisotropic time delay. Reaction–diffusion PDEs with either constant or variable transfer coefficients are considered.
Andrei D. Polyanin, Vsevolod G. Sorokin
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Fast and Slow Decaying Solutions of Lane–Emden Equations Involving Nonhomogeneous Potential
Advanced Nonlinear Studies, 2020 Our purpose in this paper is to study positive solutions of the Lane–Emden ...
Chen Huyuan, Huang Xia, Zhou Feng
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Comments on whether nonlinear fractional partial differential equations have soliton solutions
Partial Differential Equations in Applied Mathematics, 2022 It is well known that many nonlinear integer-order partial differential equations (PDEs) have soliton solutions, this is an indisputable fact in the field of soliton theory.
Weiguo Rui
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An ALE ESFEM for solving PDEs on evolving surfaces [PDF]
, 2012 Numerical methods for approximating the solution of partial differential equations on evolving hypersurfaces using surface finite elements on evolving triangulated surfaces are presented.
Vanessa Styles (4460662) +3 more
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Quantitative Predictive Modelling Approaches to Understanding Rheumatoid Arthritis: A Brief Review
Cells, 2019 Rheumatoid arthritis is a chronic autoimmune disease that is a major public health challenge. The disease is characterised by inflammation of synovial joints and cartilage erosion, which lead to chronic pain, poor life quality and, in some cases ...
Fiona R. Macfarlane +2 more
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Unsupervised Legendre–Galerkin Neural Network for Solving Partial Differential Equations
IEEE Access, 2023 In recent years, machine learning methods have been used to solve partial differential equations (PDEs) and dynamical systems, leading to the development of a new research field called scientific machine learning, which combines techniques such as deep ...
Junho Choi, Namjung Kim, Youngjoon Hong
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Neighborhood filters and PDE’s [PDF]
Numerische Mathematik, 2006 Denoising images can be achieved by a spatial averaging of nearby pixels. However, although this method removes noise it creates blur. Hence, neighborhood filters are usually preferred. These filters perform an average of neighboring pixels, but only under the condition that their grey level is close enough to the one of the pixel in restoration.
Antoni Buades +2 more
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Non-linear coupled CNN models for multiscale image analysis [PDF]
, 2006 A CNN model of partial differential equations (PDEs) for image multiscale analysis is proposed. The model is based on a polynomial representation of the diffusivity function and defines a paradigm of polynomial CNNs,for approximating a large class of ...
Corinto, Fernando +2 more
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PDE-Net: Learning PDEs from Data
CoRR, 2017 In this paper, we present an initial attempt to learn evolution PDEs from data. Inspired by the latest development of neural network designs in deep learning, we propose a new feed-forward deep network, called PDE-Net, to fulfill two objectives at the same time: to accurately predict dynamics of complex systems and to uncover the underlying hidden PDE ...
Zichao Long +3 more
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Approximate Symmetries and Conservation Laws for Mechanical Systems Described by Mixed Derivative Perturbed PDEs [PDF]
, 2023 This article focuses on developing and applying approximation techniques to derive conservation laws for the Timoshenko–Prescott mixed derivatives perturbed partial differential equations (PDEs).
Shamaoon A. +3 more
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