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nonuniqueness of Solutions of a Class of0-minimization Problems

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Journal of the Operations Research Society of China 2021年第4期9卷 893-908页

作者： Jia-Liang Xu Hua Loo-Keng Center for Mathematical Sciences Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China

Recently,finding the sparsest solution of an underdetermined linear system has become an important request in many areas such as compressed sensing,image processing,statistical learning,and data sparse *** this paper,we study some theoretical properties of the solutions to a general class of0-minimization problems,which can be used to deal with many practical *** establish some necessary conditions for a point being the sparsest solution to this class of problems,and we also characterize the conditions for the multiplicity of the sparsest solutions to the ***,we discuss certain conditions for the boundedness of the solution set of this class of problems.

关键词： 0-minimization Sparsity nonuniqueness Boundedness

Existence and nonuniqueness of Weak Solutions of the Initial-Boundary Value Problem for u_t = u~σdiv(|u|^(p-2)u)

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Northeastern Mathematical Journal 2005年第2期21卷 189-206页

作者：周文书伍卓群 School of Mathematics Jilin University Changchun 130012

In this paper, we study the existence and nonuniqueness of weak solutions of the initial and boundary value problem for ut= uσdiv(|△u|p-2△u) with σ≥1. Localization property of weak solutions is also discussed.

关键词： divergence form degenerate parabolic equation existence nonuniqueness localization

Delusions in Theoretical Hydrodynamics

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World Journal of Mechanics 2018年第9期8卷 387-415页

作者： Alexander Ivanchin Orpheus Ltd Tomsk Russia

Theoretical hydrodynamics may lead one into serious delusions. This article is focused on three of them. First, using flowing around a sphere as an example it is shown that the known potential solutions of the flow-around problems are not unique and there exist nonpotential solutions. A nonpotential solution has been obtained for flowing around a sphere. A general solution of the problem of flowing around an arbitrary surface has been obtained in the quadrature form. To single out a physically realisable solution among a great number of others, it is necessary to add supplementary conditions to the known boundary ones, in particular, to find a solution with the minimum total energy. The hypothesis explaining the reason for stalled flows by viscosity is erroneous. When considering a flow-around problem one should use stalled and broken solutions of the continuity equation along with the continuous ones. If the minimum total energy is achieved by the continuous solution, it is a continuous flow that will be implemented. If it is achieved by the broken solution, a stalled flow will be realised. Second, the hydrodynamics of a flow is considered exclusively at each point of it. Differential equations are used to describe the flows that are written for a randomly small volume of a flow, i.e., for a point. The integral characteristics of a flow and its inertial properties are neglected in the consideration, which results in the misunderstanding of the mechanism of the formation of a vortex. The reason for the formation of vortices is related to viscosity, which is a mistake. The formation of vortices is the result of the inhomogeneity of the acceleration field and the inertial properties of a flow. Third, the fictitious values of viscous stresses are used in hydrodynamics. As a matter of fact, viscosity is the momentum diffusion and it should be described by the diffusion equation included into the Euler system of equations for a viscous fluid. The momentum diffusion leads

关键词： Nonpotential Flow Around nonuniqueness of Flow around a Sphere Flow around Arbitrary Bodies Eddy Formation Viscous Flow Diffusion and Viscosity Viscous Flow along a Plate

Numerical Approximation of Real Finite Nonnegative Function by the Modulus of Discrete Fourier Transform

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Applied Mathematics 2010年第1期1卷 65-75页

作者： Petro Savenko Myroslava Tkach Pidstryhach Institute for Applied Problems of Mechanics and Mathematics National Academy of Sciences of Ukraine Lviv Ukraine

The numerical algorithms for finding the lines of branching and branching-off solutions of nonlinear problem on mean-square approximation of a real finite nonnegative function with respect to two variables by the modu... 详细信息

关键词： Mean-Square Approximation Discrete Fourier Transform Two-Dimensional Nonlinear Integral Equation nonuniqueness And Branching of Solutions

Numerical Solution of Mean-Square Approximation Problem of Real Nonnegative Function by the Modulus of Double Fourier Integral

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Applied Mathematics 2011年第9期2卷 1076-1090页

作者： Petro Savenko Myroslava Tkach 不详

A nonlinear problem of mean-square approximation of a real nonnegative continuous function with respect to two variables by the modulus of double Fourier integral dependent on two real parameters with use of the smoothing functional is studied. Finding the optimal solutions of this problem is reduced to solution of the Hammerstein type two-dimensional nonlinear integral equation. The numerical algorithms to find the branching lines and branching-off solutions of this equation are constructed and justified. Numerical examples are presented.

关键词： Mean-Square Approximation Discrete Fourier Transform Two-Dimensional Nonlinear Integral Equation nonuniqueness and Branching of Solutions Two-Dimensional Nonlinear Spectral Problem