Inverse Source Problem for a Semilinear Fractional Diffusion-Wave Equation Under a Time-Integral Condition

Abstract

We study the inverse boundary value problem on determining a space-dependent component in the right-hand side of semilinear time fractional diffusion-wave equation. We find sufficient conditions for a time-local uniqueness of the solution under the time-integral additional condition \[\frac{1}{T}\int_{0}^{T}u(x,t)\eta_1(t)dt=\Phi_1(x), \;\;\;x\in \Omega\subset \Bbb R^n\] where $u$ is the unknown solution of the first boundary value problem for such equation, $\eta_1$ and $\Phi_1$ are the given functions. We use the method of the Green's function.