2017
Том 69
№ 7

All Issues

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

Lopushanskaya G. P., Lopushanskyi A. O.

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Abstract

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].

English version (Springer): Ukrainian Mathematical Journal 66 (2014), no. 5, pp 743-757.

Citation Example: Lopushanskaya G. P., Lopushanskyi A. O. One Inverse Problem for the Diffusion-Wave Equation in Bounded Domain // Ukr. Mat. Zh. - 2014. - 66, № 5. - pp. 666–678.

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