On the inverse problem of simultaneous determination of thermal conductivity and specific heat capacity (Q1920773)

The inverse problem of simultaneous determination of the thermal conductivity and specific heat capacity in heat equation problems is discussed in a couple of papers, where the unknown functions may depend on temperature or on the space variable. In this paper, the case of time-dependent parameter functions is established. There are given conditions for existence and uniqueness of the problem of determining the unknowns \(\{c_\nu (t), \lambda (t),u(x,t)\}\) from \[ c_\nu(t) u_t = \lambda (t)u_{xx},\;0<x<h, \;0<t<T, \quad u(x,0) = \varphi (x),\;0 \leq x\leq h, \] \[ u(0,T) = \mu_1(t), \quad u(h,T) = \mu_2 (t), \quad \lambda (t)u_x (0,t) = \nu_1(t), \quad \lambda (t)u_x(h,t) = \nu_2 (t), 0\leq t\leq T. \]