Halyna Lopushanska, Vitalia Rapita
Abstract:
We establish the unique solvability for an inverse problem for semi-linear
fractional telegraph equation
![$$
D^\alpha_t u+r(t)D^\beta_t u-\Delta u=F_0(x,t,u,D^\beta_t u), \quad
(x,t) \in \Omega_0\times (0,T]
$$](gifs/aa.gif)
with regularized fractional derivatives
of orders
,
with respect to time on bounded cylindrical
domain. This problem consists in the determination of a pair of functions:
a classical solution
of the first
boundary-value problem for such equation,
and an unknown continuous coefficient
under the over-determination
condition
![$$
\int_{\Omega_0}u(x,t)\varphi(x)dx=F(t), \quad t\in [0,T]
$$](gifs/ag.gif)
with given functions
and
.
Submitted April 22, 2015. Published June 11, 2015.
Math Subject Classifications: 35S15.
Key Words: Fractional derivative; inverse boundary value problem;
over-determination integral condition; Green's function;
integral equation.
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Halyna Lopushanska Department of Differential Equations Ivan Franko National University of Lviv Lviv, Ukraine email: lhp@ukr.net |
|---|---|
| Vitalia Rapita Department of Differential Equations Ivan Franko National University of Lviv Lviv, Ukraine email: vrapita@gmail.com |
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