This article investigates the well posedness and asymptotic behavior of Neumann initial boundary value problems for a class of pseudo-parabolic equations with singular potential and logarithmic nonlinearity. By utiliz...This article investigates the well posedness and asymptotic behavior of Neumann initial boundary value problems for a class of pseudo-parabolic equations with singular potential and logarithmic nonlinearity. By utilizing cut-off techniques and combining with the Faedo Galerkin approximation method, local solvability was established. Based on the potential well method and Hardy Sobolev inequality, derive the global existence of the solution. In addition, we also obtained the results of decay.展开更多
We consider the logarithmic elliptic equation with singular nonlinearity {Δu+ulogu^(2)+λ/u^(γ)=0,in Ω,u>0,in Ω,u=0,on δΩ,where Ω⊂R^(N)(N≥3)is a bounded domain with a smooth boundary,0<γ<1 andλis a ...We consider the logarithmic elliptic equation with singular nonlinearity {Δu+ulogu^(2)+λ/u^(γ)=0,in Ω,u>0,in Ω,u=0,on δΩ,where Ω⊂R^(N)(N≥3)is a bounded domain with a smooth boundary,0<γ<1 andλis a positive constant.By using a variational method and the critical point theory for a nonsmooth functional,we obtain the existence of two positive solutions.This result generalizes and improves upon recent results in the literature.展开更多
In this paper,we study the Dirichlet problem for a class of semi-linear infinitely degenerate elliptic equations with singular potential term.By using the logarithmic Sobolev inequality and Hardy's inequality,the ...In this paper,we study the Dirichlet problem for a class of semi-linear infinitely degenerate elliptic equations with singular potential term.By using the logarithmic Sobolev inequality and Hardy's inequality,the existence and regularity of multiple nontrivial solutions have been proved.展开更多
We propose a fully discrete fast Fourier-Galerkin method for solving an integral equation of the first kind with a logarithmic kernel on a smooth open arc,which is a reformulation of the Dirichlet problem of the Lapla...We propose a fully discrete fast Fourier-Galerkin method for solving an integral equation of the first kind with a logarithmic kernel on a smooth open arc,which is a reformulation of the Dirichlet problem of the Laplace equation in the plane.The optimal convergence order and quasi-linear complexity order of the proposed method are established.A precondition is introduced.Combining this method with an efficient numerical integration algorithm for computing the single-layer potential defined on an open arc,we obtain the solution of the Dirichlet problem on a smooth open arc in the plane.Numerical examples are presented to confirm the theoretical estimates and to demonstrate the efficiency and accuracy of the proposed method.展开更多
In the paper, the approximate solution for the two-dimensional linear and nonlinear Volterra-Fredholm integral equation (V-FIE) with singular kernel by utilizing the combined Laplace-Adomian decomposition method (LADM...In the paper, the approximate solution for the two-dimensional linear and nonlinear Volterra-Fredholm integral equation (V-FIE) with singular kernel by utilizing the combined Laplace-Adomian decomposition method (LADM) was studied. This technique is a convergent series from easily computable components. Four examples are exhibited, when the kernel takes Carleman and logarithmic forms. Numerical results uncover that the method is efficient and high accurate.展开更多
A new watermarking algorithm resisting to geometric transformation based on singular value decomposition （SVD） in logarithm polar coordinate is proposed. The log-polar mapping （LPM） is used to resist rotation and ...A new watermarking algorithm resisting to geometric transformation based on singular value decomposition （SVD） in logarithm polar coordinate is proposed. The log-polar mapping （LPM） is used to resist rotation and scaling attacks, and the odd-even quantization algorithm is used to embed watermark so it can be extracted without the original host image. The experiments show that the proposed algorithm not only resists various geomet- ric attacks but also is robust enough to the common signal processing.展开更多
文摘This article investigates the well posedness and asymptotic behavior of Neumann initial boundary value problems for a class of pseudo-parabolic equations with singular potential and logarithmic nonlinearity. By utilizing cut-off techniques and combining with the Faedo Galerkin approximation method, local solvability was established. Based on the potential well method and Hardy Sobolev inequality, derive the global existence of the solution. In addition, we also obtained the results of decay.
基金supported by Natural Science Foundation of Guizhou Minzu University(20185773-YB03)supported by Fundamental Research Funds of China West Normal University(18B015)+2 种基金Innovative Research Team of China West Normal University(CXTD2018-8)supported by National Natural Science Foundation of China(11861021)supported by National Natural Science Foundation of China(11661021)。
文摘We consider the logarithmic elliptic equation with singular nonlinearity {Δu+ulogu^(2)+λ/u^(γ)=0,in Ω,u>0,in Ω,u=0,on δΩ,where Ω⊂R^(N)(N≥3)is a bounded domain with a smooth boundary,0<γ<1 andλis a positive constant.By using a variational method and the critical point theory for a nonsmooth functional,we obtain the existence of two positive solutions.This result generalizes and improves upon recent results in the literature.
基金supported by National Natural Science Foundation of China (Grant No.11131005)PHD Programs Foundation of Ministry of Education of China (Grant No. 20090141110003)the Fundamental Research Funds for the Central Universities (Grant No. 2012201020202)
文摘In this paper,we study the Dirichlet problem for a class of semi-linear infinitely degenerate elliptic equations with singular potential term.By using the logarithmic Sobolev inequality and Hardy's inequality,the existence and regularity of multiple nontrivial solutions have been proved.
基金supported by the President Fund of GUCAS and the US National Science Foundation (Grant No.CCR-0407476,DMS-0712827)National Natural Science Foundation of China(Grant No.10371122,10631080)
文摘We propose a fully discrete fast Fourier-Galerkin method for solving an integral equation of the first kind with a logarithmic kernel on a smooth open arc,which is a reformulation of the Dirichlet problem of the Laplace equation in the plane.The optimal convergence order and quasi-linear complexity order of the proposed method are established.A precondition is introduced.Combining this method with an efficient numerical integration algorithm for computing the single-layer potential defined on an open arc,we obtain the solution of the Dirichlet problem on a smooth open arc in the plane.Numerical examples are presented to confirm the theoretical estimates and to demonstrate the efficiency and accuracy of the proposed method.
文摘In the paper, the approximate solution for the two-dimensional linear and nonlinear Volterra-Fredholm integral equation (V-FIE) with singular kernel by utilizing the combined Laplace-Adomian decomposition method (LADM) was studied. This technique is a convergent series from easily computable components. Four examples are exhibited, when the kernel takes Carleman and logarithmic forms. Numerical results uncover that the method is efficient and high accurate.
基金Supported by the National Natural Science Foundation of China (60842006)
文摘A new watermarking algorithm resisting to geometric transformation based on singular value decomposition （SVD） in logarithm polar coordinate is proposed. The log-polar mapping （LPM） is used to resist rotation and scaling attacks, and the odd-even quantization algorithm is used to embed watermark so it can be extracted without the original host image. The experiments show that the proposed algorithm not only resists various geomet- ric attacks but also is robust enough to the common signal processing.
