On the backward heat problem: evaluation of the norm of ∂u∂t
We show in this paper that ‖Δu‖=‖ut‖ is bounded ∀t≤T(0)<T if one imposes on u (solution of the backward heat equation) the condition ‖u(x,t)‖≤M. A Hölder type of inequality is also given if one supposes ‖ut(x,T)‖≤K.
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| Format: | Article |
| Language: | English |
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Wiley
1980-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171280000464 |
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| _version_ | 1850169320443740160 |
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| author | Yves Biollay |
| author_facet | Yves Biollay |
| author_sort | Yves Biollay |
| collection | DOAJ |
| description | We show in this paper that ‖Δu‖=‖ut‖ is bounded ∀t≤T(0)<T if one imposes on u (solution of the backward heat equation) the condition ‖u(x,t)‖≤M. A Hölder type of inequality is also given if one supposes ‖ut(x,T)‖≤K. |
| format | Article |
| id | doaj-art-a8a74a7b781b40208cd84ed567a5f6bc |
| institution | OA Journals |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1980-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-a8a74a7b781b40208cd84ed567a5f6bc2025-08-20T02:20:45ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251980-01-013359960310.1155/S0161171280000464On the backward heat problem: evaluation of the norm of ∂u∂tYves Biollay0Department of Mathematics, Cornell University, Ithaca, New York 14850, USAWe show in this paper that ‖Δu‖=‖ut‖ is bounded ∀t≤T(0)<T if one imposes on u (solution of the backward heat equation) the condition ‖u(x,t)‖≤M. A Hölder type of inequality is also given if one supposes ‖ut(x,T)‖≤K.http://dx.doi.org/10.1155/S0161171280000464parabolic equationsimproperly posed problems. |
| spellingShingle | Yves Biollay On the backward heat problem: evaluation of the norm of ∂u∂t International Journal of Mathematics and Mathematical Sciences parabolic equations improperly posed problems. |
| title | On the backward heat problem: evaluation of the norm of ∂u∂t |
| title_full | On the backward heat problem: evaluation of the norm of ∂u∂t |
| title_fullStr | On the backward heat problem: evaluation of the norm of ∂u∂t |
| title_full_unstemmed | On the backward heat problem: evaluation of the norm of ∂u∂t |
| title_short | On the backward heat problem: evaluation of the norm of ∂u∂t |
| title_sort | on the backward heat problem evaluation of the norm of ∂u∂t |
| topic | parabolic equations improperly posed problems. |
| url | http://dx.doi.org/10.1155/S0161171280000464 |
| work_keys_str_mv | AT yvesbiollay onthebackwardheatproblemevaluationofthenormofut |