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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Hindawi Limited
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 |
| Summary: | 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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| ISSN: | 0161-1712 1687-0425 |