Novel exact solutions for PDEs with mixed boundary conditions
Abstract We develop methods for the solution of inhomogeneous Robin-type boundary value problems (BVPs) that arise for certain linear parabolic partial differential equations (PDEs) on a half-line, as well as a second-order generalization. We are able to obtain nonstandard solutions to equations ari...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2025-01-01
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| Series: | Boundary Value Problems |
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| Online Access: | https://doi.org/10.1186/s13661-024-01989-2 |
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| _version_ | 1832585528414830592 |
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| author | Mark Craddock Martino Grasselli Andrea Mazzoran |
| author_facet | Mark Craddock Martino Grasselli Andrea Mazzoran |
| author_sort | Mark Craddock |
| collection | DOAJ |
| description | Abstract We develop methods for the solution of inhomogeneous Robin-type boundary value problems (BVPs) that arise for certain linear parabolic partial differential equations (PDEs) on a half-line, as well as a second-order generalization. We are able to obtain nonstandard solutions to equations arising in a range of areas, including mathematical finance, stochastic analysis, hyperbolic geometry, and mathematical physics. Our approach uses the odd and even Hilbert transforms. The solutions we obtain and the method itself seem to be new. |
| format | Article |
| id | doaj-art-db135ba209a14d80b0860e3409f8ecbb |
| institution | Kabale University |
| issn | 1687-2770 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Boundary Value Problems |
| spelling | doaj-art-db135ba209a14d80b0860e3409f8ecbb2025-01-26T12:45:01ZengSpringerOpenBoundary Value Problems1687-27702025-01-012025113810.1186/s13661-024-01989-2Novel exact solutions for PDEs with mixed boundary conditionsMark Craddock0Martino Grasselli1Andrea Mazzoran2School of Mathematical and Physical Sciences, University of Technology SydneyDepartment of Mathematics “Tullio Levi Civita”, University of PadovaDepartment of Mathematics “Tullio Levi Civita”, University of PadovaAbstract We develop methods for the solution of inhomogeneous Robin-type boundary value problems (BVPs) that arise for certain linear parabolic partial differential equations (PDEs) on a half-line, as well as a second-order generalization. We are able to obtain nonstandard solutions to equations arising in a range of areas, including mathematical finance, stochastic analysis, hyperbolic geometry, and mathematical physics. Our approach uses the odd and even Hilbert transforms. The solutions we obtain and the method itself seem to be new.https://doi.org/10.1186/s13661-024-01989-2Fundamental solutionsParabolic PDEsBoundary value problemsLaplace transformFourier transformHilbert transform |
| spellingShingle | Mark Craddock Martino Grasselli Andrea Mazzoran Novel exact solutions for PDEs with mixed boundary conditions Boundary Value Problems Fundamental solutions Parabolic PDEs Boundary value problems Laplace transform Fourier transform Hilbert transform |
| title | Novel exact solutions for PDEs with mixed boundary conditions |
| title_full | Novel exact solutions for PDEs with mixed boundary conditions |
| title_fullStr | Novel exact solutions for PDEs with mixed boundary conditions |
| title_full_unstemmed | Novel exact solutions for PDEs with mixed boundary conditions |
| title_short | Novel exact solutions for PDEs with mixed boundary conditions |
| title_sort | novel exact solutions for pdes with mixed boundary conditions |
| topic | Fundamental solutions Parabolic PDEs Boundary value problems Laplace transform Fourier transform Hilbert transform |
| url | https://doi.org/10.1186/s13661-024-01989-2 |
| work_keys_str_mv | AT markcraddock novelexactsolutionsforpdeswithmixedboundaryconditions AT martinograsselli novelexactsolutionsforpdeswithmixedboundaryconditions AT andreamazzoran novelexactsolutionsforpdeswithmixedboundaryconditions |