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One Inverse Problem for the Diffusion-Wave Equation in Bounded Domain

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Ukrainian Mathematical Journal Aims and scope

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 β t 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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Authors and Affiliations

  1. Rzeszów University, Rzeszów, Poland

    A. O. Lopushanskyi & H. P. Lopushanska

  2. Lviv University, Lviv, Ukraine

    A. O. Lopushanskyi & H. P. Lopushanska

Authors
  1. A. O. Lopushanskyi
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  2. H. P. Lopushanska
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 66, No. 5, pp. 666–678, May, 2014.

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Lopushanskyi, A.O., Lopushanska, H.P. One Inverse Problem for the Diffusion-Wave Equation in Bounded Domain. Ukr Math J 66, 743–757 (2014). https://doi.org/10.1007/s11253-014-0969-9

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  • DOI: https://doi.org/10.1007/s11253-014-0969-9

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