Homotopy analysis method for discrete quasi-reversibility mollification method of nonhomogeneous backward heat conduction problem [PDF]
Nonlinear Engineering, 2023 In this article, the inverse time problem is investigated. Regarding the ill-posed linear problem, utilize the quasi-reversibility method first. This problem has been regularized and after that provides an iterative regularizing strategy for noisy input ...
Rahimi Mostafa, Rostamy Davood
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A Mollification Regularization Method for the Inverse Source Problem for a Time Fractional Diffusion Equation [PDF]
Mathematics, 2019 We consider a time-fractional diffusion equation for an inverse problem to determine an unknown source term, whereby the input data is obtained at a certain time. In general, the inverse problems are ill-posed in the sense of Hadamard. Therefore, in this
Le Dinh Long +3 more
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Robust and Fast Normal Mollification via Consistent Neighborhood Reconstruction for Unorganized Point Clouds [PDF]
Sensors, 2023 This paper introduces a robust normal estimation method for point cloud data that can handle both smooth and sharp features. Our method is based on the inclusion of neighborhood recognition into the normal mollification process in the neighborhood of the
Guangshuai Liu +3 more
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A General Mollification Regularization Method to Solve a Cauchy Problem for the Multi-Dimensional Modified Helmholtz Equation [PDF]
SymmetryThis paper considers a Cauchy problem for the multi-dimensional modified Helmholtz equation with inhomogeneous Dirichlet and Neumann data. The Cauchy problem is severely ill-posed, and a general mollification method is introduced to solve the problem. Both the a priori and a posteriori choice strategies of the regularization parameter are proposed, and
Huilin Xu, B. Wang, Duanmei Zhou
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A Jacobi spectral method for calculating fractional derivative based on mollification regularization
Asymptotic Analysis, 2023 In this article, we construct a Jacobi spectral collocation scheme to approximate the Caputo fractional derivative based on Jacobi–Gauss quadrature. The convergence analysis is provided in anisotropic Jacobi-weighted Sobolev spaces. Furthermore, the convergence rate is presented for solving Caputo fractional derivative with noisy data by invoking the ...
Wen Zhang +3 more
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A mollification method for a Cauchy problem for the Laplace equation
Applied Mathematics and Computation, 2011 The authors consider the Cauchy problem for the Laplace equation in an infinite strip \(u_{xx} + u_{yy} =0, x \in (0,1), y \in \mathbb{R}, u(0,y) = \varphi(y), u_x(0,y) = 0, y \in \mathbb{R}\) with noisy Cauchy data \(\varphi^\delta \in L^2(\mathbb{R})\).
Zhenping Li, Chu‐Li Fu
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A Mollification Regularization Method for a Fractional-Diffusion Inverse Heat Conduction Problem [PDF]
Mathematical Problems in Engineering, 2013 The ill-posed problem of attempting to recover the temperature functions from one measured transient data temperature at some interior point of a one-dimensional semi-infinite conductor when the governing linear diffusion equation is of fractional type is discussed.
Zhiliang Deng, Xiaomei Yang, Xiaoli Feng
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A mollification regularization method for the inverse spatial-dependent heat source problem
Journal of Computational and Applied Mathematics, 2013 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Fan Yang, Chu‐Li Fu
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Regularization of a nonlinear inverse problem by discrete mollification method [PDF]
, 2021 Summary: In this article, the application of discrete mollification as a regularization procedure for solving a nonlinear inverse problem in one dimensional space is considered. Illposedness is identified as one of the main characteristics of inverse problems. It is clear that if we have a noisy data, the inverse problem becomes unstable.
Soheila Bodaghi +2 more
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A Mollification Method for a Noncharacteristic Cauchy Problem for a Parabolic Equation
Journal of Mathematical Analysis and Applications, 1996 The object of this paper is the study of the following noncharactristic Cauchy problem \[ u_t-a(x)u_{xx}-b(x)u_x-c(x)u=0,\quad u(0,t)=\varphi(t),\quad u_x(0,t)=0. \] The analysis of this problem is clear and was studied by the author in previous papers, too. It is proved, that under certain assumptions for the coefficients the above problem has a \(L_p\
Ðinh Nho Hào
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