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Volume 24, Issue 2
Construction of Green's Functions for the Two-dimensional Static Klein-Gordon Equation

Yu A. Melnikov

DOI: 10.4208/jpde.v24.n2.2

J. Part. Diff. Eq., 24 (2011), pp. 114-139.

Published online: 2011-05

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  • Abstract

In contrast to the cognate Laplace equation, for which a vast number of Green's functions is available, the field is not that developed for the static Klein-Gordon equation. The latter represents, nonetheless, a natural area for application of some of the methods that are proven productive for the Laplace equation. The perspective looks especially attractive for the methods of images and eigenfunction expansion. This study is based on our experience recently gained on the construction of Green's functions for elliptic partial differential equations. An extensive list of boundary-value problems formulated for the static Klein-Gordon equation is considered. Computer-friendly representations of their Green's functions are obtained, most of which have never been published before.

  • Keywords

Static Klein-Gordon equation Green's function

  • AMS Subject Headings

35J08 65N80

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JPDE-24-114, author = {Yu A. Melnikov }, title = {Construction of Green's Functions for the Two-dimensional Static Klein-Gordon Equation}, journal = {Journal of Partial Differential Equations}, year = {2011}, volume = {24}, number = {2}, pages = {114--139}, abstract = {

In contrast to the cognate Laplace equation, for which a vast number of Green's functions is available, the field is not that developed for the static Klein-Gordon equation. The latter represents, nonetheless, a natural area for application of some of the methods that are proven productive for the Laplace equation. The perspective looks especially attractive for the methods of images and eigenfunction expansion. This study is based on our experience recently gained on the construction of Green's functions for elliptic partial differential equations. An extensive list of boundary-value problems formulated for the static Klein-Gordon equation is considered. Computer-friendly representations of their Green's functions are obtained, most of which have never been published before.

}, issn = {2079-732X}, doi = {https://doi.org/10.4208/jpde.v24.n2.2}, url = {http://global-sci.org/intro/article_detail/jpde/5201.html} }
TY - JOUR T1 - Construction of Green's Functions for the Two-dimensional Static Klein-Gordon Equation AU - Yu A. Melnikov JO - Journal of Partial Differential Equations VL - 2 SP - 114 EP - 139 PY - 2011 DA - 2011/05 SN - 24 DO - http://doi.org/10.4208/jpde.v24.n2.2 UR - https://global-sci.org/intro/article_detail/jpde/5201.html KW - Static Klein-Gordon equation KW - Green's function AB -

In contrast to the cognate Laplace equation, for which a vast number of Green's functions is available, the field is not that developed for the static Klein-Gordon equation. The latter represents, nonetheless, a natural area for application of some of the methods that are proven productive for the Laplace equation. The perspective looks especially attractive for the methods of images and eigenfunction expansion. This study is based on our experience recently gained on the construction of Green's functions for elliptic partial differential equations. An extensive list of boundary-value problems formulated for the static Klein-Gordon equation is considered. Computer-friendly representations of their Green's functions are obtained, most of which have never been published before.

Yu A. Melnikov . (2011). Construction of Green's Functions for the Two-dimensional Static Klein-Gordon Equation. Journal of Partial Differential Equations. 24 (2). 114-139. doi:10.4208/jpde.v24.n2.2
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