Conservation laws that depend on functions and PDE reduction: Extending Noether $1\tfrac {1}{2}$
This paper develops methods for simplifying systems of partial differential equations (PDEs) that have families of conservation laws which depend on arbitrary functions of the independent or dependent variables. Cases are identified in which such methods can be combined with reduction using families...
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| Format: | Article |
| Language: | English |
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Cambridge University Press
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| Series: | European Journal of Applied Mathematics |
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| Online Access: | https://www.cambridge.org/core/product/identifier/S0956792525100090/type/journal_article |
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| author | Peter E. Hydon John R. King |
| author_facet | Peter E. Hydon John R. King |
| author_sort | Peter E. Hydon |
| collection | DOAJ |
| description | This paper develops methods for simplifying systems of partial differential equations (PDEs) that have families of conservation laws which depend on arbitrary functions of the independent or dependent variables. Cases are identified in which such methods can be combined with reduction using families of symmetries to give a multiple reduction; this is analogous to the double reduction of order for ordinary differential equations (ODE) with variational symmetries. Applications are given, including a widely used class of pseudoparabolic equations and several mean curvature equations. |
| format | Article |
| id | doaj-art-8d29e86261cf4ecb8e4ceed976f62b37 |
| institution | Kabale University |
| issn | 0956-7925 1469-4425 |
| language | English |
| publisher | Cambridge University Press |
| record_format | Article |
| series | European Journal of Applied Mathematics |
| spelling | doaj-art-8d29e86261cf4ecb8e4ceed976f62b372025-08-20T03:59:30ZengCambridge University PressEuropean Journal of Applied Mathematics0956-79251469-442511810.1017/S0956792525100090Conservation laws that depend on functions and PDE reduction: Extending Noether $1\tfrac {1}{2}$Peter E. Hydon0https://orcid.org/0000-0002-3732-4813John R. King1https://orcid.org/0000-0002-6228-8375School of Mathematics, Statistics and Actuarial Science, University of Kent, Canterbury, UKSchool of Mathematical Sciences, University of Nottingham, Nottingham, UKThis paper develops methods for simplifying systems of partial differential equations (PDEs) that have families of conservation laws which depend on arbitrary functions of the independent or dependent variables. Cases are identified in which such methods can be combined with reduction using families of symmetries to give a multiple reduction; this is analogous to the double reduction of order for ordinary differential equations (ODE) with variational symmetries. Applications are given, including a widely used class of pseudoparabolic equations and several mean curvature equations.https://www.cambridge.org/core/product/identifier/S0956792525100090/type/journal_articleConservation LawsPDE reductionsymmetries35A2535A1537K0670H3353E10 |
| spellingShingle | Peter E. Hydon John R. King Conservation laws that depend on functions and PDE reduction: Extending Noether $1\tfrac {1}{2}$ European Journal of Applied Mathematics Conservation Laws PDE reduction symmetries 35A25 35A15 37K06 70H33 53E10 |
| title | Conservation laws that depend on functions and PDE reduction: Extending Noether $1\tfrac {1}{2}$ |
| title_full | Conservation laws that depend on functions and PDE reduction: Extending Noether $1\tfrac {1}{2}$ |
| title_fullStr | Conservation laws that depend on functions and PDE reduction: Extending Noether $1\tfrac {1}{2}$ |
| title_full_unstemmed | Conservation laws that depend on functions and PDE reduction: Extending Noether $1\tfrac {1}{2}$ |
| title_short | Conservation laws that depend on functions and PDE reduction: Extending Noether $1\tfrac {1}{2}$ |
| title_sort | conservation laws that depend on functions and pde reduction extending noether 1 tfrac 1 2 |
| topic | Conservation Laws PDE reduction symmetries 35A25 35A15 37K06 70H33 53E10 |
| url | https://www.cambridge.org/core/product/identifier/S0956792525100090/type/journal_article |
| work_keys_str_mv | AT peterehydon conservationlawsthatdependonfunctionsandpdereductionextendingnoether1tfrac12 AT johnrking conservationlawsthatdependonfunctionsandpdereductionextendingnoether1tfrac12 |