Inverse problem of simultaneous determination of two coefficients in a parabolic equation (Q2730504)

The author considers the parabolic equation NEWLINE\[NEWLINE u_t=a(t)(u_{xx}+b(x)u_x)+c(x,t)u+f(x,t),\quad 0<x<h,0<t<T, NEWLINE\]NEWLINE with initial condition and Dirichlet boundary conditions. The problem of determination of two unknown coefficients \(a(t)\) and \(b(x)\) if the functions \(t\mapsto a(t)u_x(0,t)\) and \(x\mapsto \int_0^{t_0}a(\tau)u_x(x,\tau) d\tau\) are given, is studied. Here \(t_0\) is a fixed number.