One Inverse Problem for the Diffusion-Wave Equation in Bounded Domain
We prove the theorems on the existence and unique determination of a pair of functions: a(t) >0, t ∈ [0,T], and the solution u(x, t) of the first boundary-value problem for the equation $$ \begin{array}{ll}{D}_t^{\beta }u-a(t){u}_{xx}={F}_0\left(x,t\right),\hfill & \left(x,t\right)\i...
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| Date: | 2014 |
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| Main Authors: | , , , |
| Format: | Article |
| Language: | Ukrainian English |
| Published: |
Institute of Mathematics, NAS of Ukraine
2014
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/2168 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
| Download file: |  |
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Ukrains’kyi Matematychnyi Zhurnal| Summary: | We prove the theorems on the existence and unique determination of a pair of functions: a(t) >0, t ∈ [0,T], and the solution u(x, t) of the first boundary-value problem for the equation $$ \begin{array}{ll}{D}_t^{\beta }u-a(t){u}_{xx}={F}_0\left(x,t\right),\hfill & \left(x,t\right)\in \left(0,l\right)\times \left(0,T\right],\hfill \end{array} $$ with regularized derivative D t β u of the fractional order β ∈ (0, 2) under the additional condition a(t)u x (0, t) = F(t), t ∈ [0,T]. |
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