Well-posedness of heat and wave equations generated by Rubin’s q-difference operator in Sobolev spaces
In this paper, we investigate difference-differential operators of parabolic and hyperbolic types. Namely, we consider non-homogenous heat and wave equations for Rubin’s difference operator. Well-posedness results are obtained in appropriate Sobolev type spaces. In particular, we prove that the heat...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2023 |
| País: | España |
| Institución: | Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya) |
| Repositorio: | Recercat. Dipósit de la Recerca de Catalunya |
| OAI Identifier: | oai:recercat.cat:2072/535766 |
| Acceso en línea: | http://hdl.handle.net/2072/535766 |
| Access Level: | acceso abierto |
| Palabra clave: | A priori estimate Heat equation, wave equation q-calculus q-derivative q-difference operator Rubin difference operator Sobolev type space Well-posedness |
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oai:recercat.cat:2072/535766 |
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España |
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Well-posedness of heat and wave equations generated by Rubin’s q-difference operator in Sobolev spaces Shaimardan, S. Persson, L.-E. Tokmagambetov, N. A priori estimate Heat equation, wave equation q-calculus q-derivative q-difference operator Rubin difference operator Sobolev type space Well-posedness In this paper, we investigate difference-differential operators of parabolic and hyperbolic types. Namely, we consider non-homogenous heat and wave equations for Rubin’s difference operator. Well-posedness results are obtained in appropriate Sobolev type spaces. In particular, we prove that the heat and wave equations generated by Rubin’s difference operator have unique solutions. We even show that these solutions can be represented by explicit formulas. © 2023, University of Nis. All rights reserved. Ministry of Education and Science of the Republic of Kazakhstan: AP08052208. This work also acknowledges the CERCA Programme of the Generalitat de Catalunya for institutional support. This work was also supported by the Spanish State Research Agency, through the Severo Ochoa and Maria de Maeztu Program for Centres and Units of Excellence in R&D (CEX2020-001084-M). University of Nis http://hdl.handle.net/2072/535766 |
| title |
Well-posedness of heat and wave equations generated by Rubin’s q-difference operator in Sobolev spaces |
| spellingShingle |
Well-posedness of heat and wave equations generated by Rubin’s q-difference operator in Sobolev spaces Shaimardan, S. A priori estimate Heat equation, wave equation q-calculus q-derivative q-difference operator Rubin difference operator Sobolev type space Well-posedness |
| title_short |
Well-posedness of heat and wave equations generated by Rubin’s q-difference operator in Sobolev spaces |
| title_full |
Well-posedness of heat and wave equations generated by Rubin’s q-difference operator in Sobolev spaces |
| title_fullStr |
Well-posedness of heat and wave equations generated by Rubin’s q-difference operator in Sobolev spaces |
| title_full_unstemmed |
Well-posedness of heat and wave equations generated by Rubin’s q-difference operator in Sobolev spaces |
| title_sort |
Well-posedness of heat and wave equations generated by Rubin’s q-difference operator in Sobolev spaces |
| author |
Shaimardan, S. |
| author_facet |
Shaimardan, S. Persson, L.-E. Tokmagambetov, N. |
| author_role |
author |
| author2 |
Persson, L.-E. Tokmagambetov, N. |
| author2_role |
author author |
| topic |
A priori estimate Heat equation, wave equation q-calculus q-derivative q-difference operator Rubin difference operator Sobolev type space Well-posedness |
| topic_facet |
A priori estimate Heat equation, wave equation q-calculus q-derivative q-difference operator Rubin difference operator Sobolev type space Well-posedness |
| description |
In this paper, we investigate difference-differential operators of parabolic and hyperbolic types. Namely, we consider non-homogenous heat and wave equations for Rubin’s difference operator. Well-posedness results are obtained in appropriate Sobolev type spaces. In particular, we prove that the heat and wave equations generated by Rubin’s difference operator have unique solutions. We even show that these solutions can be represented by explicit formulas. © 2023, University of Nis. All rights reserved. |
| publishDate |
2023 |
| format |
article |
| status_str |
publishedVersion |
| url |
http://hdl.handle.net/2072/535766 |
| eu_rights_str_mv |
openAccess |
| publisher |
University of Nis |
| institution |
Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya) |
| collection |
Recercat. Dipósit de la Recerca de Catalunya |
| reponame_str |
Recercat. Dipósit de la Recerca de Catalunya |
| instname_str |
Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya) |
| _version_ |
1878436967536918528 |
| publishDateSort |
2023 |
| author_browse |
Persson, L.-E. Shaimardan, S. Tokmagambetov, N. |
| publisherStr |
University of Nis |
| score |
6,9303427 |