inverse coefficient problem for the semi-linear fractional telegraph equation
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ID: 196511
2015
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Abstract
We establish the unique solvability for an inverse problem for semi-linear
fractional telegraph equation
$$
D^\alpha_t u+r(t)D^\beta_t u-\Delta u=F_0(x,t,u,D^\beta_t u), \quad
(x,t) \in \Omega_0\times (0,T]
$$
with regularized fractional derivatives $D^\alpha_t u, D^\beta_t u$ of orders
$\alpha\in (1,2)$, $\beta\in (0,1)$ with respect to time on bounded cylindrical
domain. This problem consists in the determination of a pair of functions:
a classical solution $u$ of the first boundary-value problem for such equation,
and an unknown continuous coefficient $r(t)$ under the over-determination
condition
$$
\int_{\Omega_0}u(x,t)\varphi(x)dx=F(t), \quad t\in [0,T]
$$
with given functions $\varphi$ and $F$.
| Reference Key |
lopushanska2015electronicinverse
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|---|---|
| Authors | ;Halyna Lopushanska;Vitalia Rapita |
| Journal | icsoft 2006 - 1st international conference on software and data technologies, proceedings |
| Year | 2015 |
| DOI |
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|
| URL | |
| Keywords | Keywords not found |
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