On classification and invariants of second order non-parabolic linear partial differential equations in two variables
The paper deals with second order abstract linear partial differential equations (LPDE) over a partial differential field with two commuting differential operators. In terms of usual differential equations the main content can be presented as follows. The classification and invariants problems for...
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| Format: | Proceeding Paper |
| Language: | English English English |
| Published: |
AIP
2018
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| Online Access: | http://irep.iium.edu.my/69402/ http://irep.iium.edu.my/69402/8/69402%20On%20classification%20and%20invariants%20of%20second%20order%20non-parabolic%20linear%20partial%20differential.pdf http://irep.iium.edu.my/69402/9/69402%20On%20classification%20and%20invariants%20of%20second%20order%20SCOPUS.pdf http://irep.iium.edu.my/69402/20/69402_On%20classification%20and%20invariants%20of%20second_WOS.pdf |
| _version_ | 1848787108032937984 |
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| author | Bekbaev, Ural |
| author_facet | Bekbaev, Ural |
| author_sort | Bekbaev, Ural |
| building | IIUM Repository |
| collection | Online Access |
| description | The paper deals with second order abstract linear partial differential equations (LPDE) over a partial differential
field with two commuting differential operators. In terms of usual differential equations the main content can be presented as
follows. The classification and invariants problems for second order LPDEs with respect to transformations
x = x(x ;h); y = y(x ;h); u = h(x;y)v(x ;h);
where x;y are independent and u is the dependent variable of the LPDE, are considered. Solutions to these problems are given
for different subclasses of non-parabolic LPDE which appear naturally in the equivalence problem of LPDE. A criterion for
reducibility of such LPDE to LPDE with constant coefficients is offered as well. |
| first_indexed | 2025-11-14T17:19:41Z |
| format | Proceeding Paper |
| id | iium-69402 |
| institution | International Islamic University Malaysia |
| institution_category | Local University |
| language | English English English |
| last_indexed | 2025-11-14T17:19:41Z |
| publishDate | 2018 |
| publisher | AIP |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | iium-694022019-02-21T04:11:22Z http://irep.iium.edu.my/69402/ On classification and invariants of second order non-parabolic linear partial differential equations in two variables Bekbaev, Ural Q Science (General) QA Mathematics QA300 Analysis The paper deals with second order abstract linear partial differential equations (LPDE) over a partial differential field with two commuting differential operators. In terms of usual differential equations the main content can be presented as follows. The classification and invariants problems for second order LPDEs with respect to transformations x = x(x ;h); y = y(x ;h); u = h(x;y)v(x ;h); where x;y are independent and u is the dependent variable of the LPDE, are considered. Solutions to these problems are given for different subclasses of non-parabolic LPDE which appear naturally in the equivalence problem of LPDE. A criterion for reducibility of such LPDE to LPDE with constant coefficients is offered as well. AIP 2018 Proceeding Paper PeerReviewed application/pdf en http://irep.iium.edu.my/69402/8/69402%20On%20classification%20and%20invariants%20of%20second%20order%20non-parabolic%20linear%20partial%20differential.pdf application/pdf en http://irep.iium.edu.my/69402/9/69402%20On%20classification%20and%20invariants%20of%20second%20order%20SCOPUS.pdf application/pdf en http://irep.iium.edu.my/69402/20/69402_On%20classification%20and%20invariants%20of%20second_WOS.pdf Bekbaev, Ural (2018) On classification and invariants of second order non-parabolic linear partial differential equations in two variables. In: 25th National Symposium on Mathematical Sciences (SKSM25), 27th-29th August 2017, Kuantan, Pahang. https://aip.scitation.org/doi/10.1063/1.5041578 10.1063/1.5041578 |
| spellingShingle | Q Science (General) QA Mathematics QA300 Analysis Bekbaev, Ural On classification and invariants of second order non-parabolic linear partial differential equations in two variables |
| title | On classification and invariants of second order non-parabolic linear partial differential equations in two variables |
| title_full | On classification and invariants of second order non-parabolic linear partial differential equations in two variables |
| title_fullStr | On classification and invariants of second order non-parabolic linear partial differential equations in two variables |
| title_full_unstemmed | On classification and invariants of second order non-parabolic linear partial differential equations in two variables |
| title_short | On classification and invariants of second order non-parabolic linear partial differential equations in two variables |
| title_sort | on classification and invariants of second order non-parabolic linear partial differential equations in two variables |
| topic | Q Science (General) QA Mathematics QA300 Analysis |
| url | http://irep.iium.edu.my/69402/ http://irep.iium.edu.my/69402/ http://irep.iium.edu.my/69402/ http://irep.iium.edu.my/69402/8/69402%20On%20classification%20and%20invariants%20of%20second%20order%20non-parabolic%20linear%20partial%20differential.pdf http://irep.iium.edu.my/69402/9/69402%20On%20classification%20and%20invariants%20of%20second%20order%20SCOPUS.pdf http://irep.iium.edu.my/69402/20/69402_On%20classification%20and%20invariants%20of%20second_WOS.pdf |