On mistaken papers by Gouzheng Yan et al and related papers, and on a paper by Weibing Wang and Xuxin Yang

Крутицкий, П. А.

doi:10.1002/mma.2812

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Nonexistence Of a Weak Solution1

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2014

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“…12.5], where it was referred to as the Hadamard example. Another closed-form example of such a function can be found in [14,Sec. 2].…”

Section: Nonexistence Of a Weak Solutionmentioning

confidence: 97%

Dirichlet problem for the Helmholtz equation in an exterior two-dimensional domain with cuts without matching conditions at the cut endpoints

Крутицкий

2014

Diff Equat

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The Dirichlet problem for the Helmholtz equation in a plane exterior domain with cuts is considered for the case in which functions defined on opposite sides of the cuts in the Dirichlet boundary condition do not necessarily satisfy the matching conditions at the cut endpoints and the solution of the problem is not necessarily continuous at the endpoints of the cuts. We give a well-posed statement of the problem, prove existence and uniqueness theorems for a classical solution, derive an integral representation of the solution, and use it to study its properties. We show that the Dirichlet problem in the considered setting does not necessarily have a weak solution, although there exists a classical solution. We derive asymptotic formulas describing the behavior of the gradient of the solution at the endpoints of the cuts.

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“…12.5], where it was referred to as the Hadamard example. Another closed-form example of such a function can be found in [14,Sec. 2].…”

Section: Nonexistence Of a Weak Solutionmentioning

confidence: 97%

Dirichlet problem for the Helmholtz equation in an exterior two-dimensional domain with cuts without matching conditions at the cut endpoints

Крутицкий

2014

Diff Equat

View full text Add to dashboard Cite

show abstract

On mistaken papers by Gouzheng Yan et al and related papers, and on a paper by Weibing Wang and Xuxin Yang

Abstract: The purpose of the present note is to point out mathematical mistakes in some published papers on boundary value problems to prevent usage of mistaken results and methods by mathematicians. Copyright © 2013 John Wiley & Sons, Ltd.

Cited by 1 publication

References 5 publications

Dirichlet problem for the Helmholtz equation in an exterior two-dimensional domain with cuts without matching conditions at the cut endpoints

Dirichlet problem for the Helmholtz equation in an exterior two-dimensional domain with cuts without matching conditions at the cut endpoints

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