Gözükızıl, Omer Faruk; Yaman, Metin A note on the unique solvability of an inverse problem with integral overdetermination. (English) Zbl 1161.35514 Appl. Math. E-Notes 8, 223-230 (2008). Summary: In this paper we study the unique solvability of the inverse problem of determining a pair of functions \(\{u, f\}\) satisfying the equation \[ u_t-\Delta_u + \sum^n_{i=1} b_i(x)u_{x_i} + \alpha_u = f(t)g(x, t),\quad (x,t)\in Q_T\equiv \Omega\times (0, T), \]the initial condition \[ u(x, 0) = u_0(x),\quad x\in\Omega, \]the boundary condition \[ u(x, t) = 0,\quad x\in \partial\Omega,\quad t\in(0,T) \]and the overdetermination condition \[ \int_\Omega u(x, t)w(x)\,dx =\xi(t),\quad t\in (0,T), \]where is a bounded domain in \(\mathbb R^n\) with smooth boundary \(\partial \Omega\). Cited in 5 Documents MSC: 35R30 Inverse problems for PDEs 35D05 Existence of generalized solutions of PDE (MSC2000) 35A35 Theoretical approximation in context of PDEs Keywords:inverse problem; parabolic equation; integral overdetermination condition PDFBibTeX XMLCite \textit{O. F. Gözükızıl} and \textit{M. Yaman}, Appl. Math. E-Notes 8, 223--230 (2008; Zbl 1161.35514) Full Text: EuDML EMIS