Inverse problems of determination of ionite characteristics from data of dynamic experiments (Q1177472)

The authors consider the dynamic problem for the system \[ \begin{cases} \nu u_ x+u_ t+a_ t=Du_{xx},\quad 0<x<\ell,\quad 0<t\leq T \\ a_ t=\gamma(a)(\varphi(u)-a),\quad 0<x\leq\ell,\quad 0<t\leq T \\ u(0,t)=\mu(t),\quad u(\ell,t)+\lambda u_ x(\ell,t)=0,\quad 0<t\leq T \\ u(x,0)=0,\;a(x,0)=0,\;0\leq x\leq\ell. \end{cases} \tag{*} \] Assuming certain smoothness conditions for the given parameters they define two inverse problems to \((*)\) and prove the uniqueness of their solutions \(\{u(x,t),a(x,t),\gamma(\xi)\}\) and \(\{u(x,t),a(x,t)\), \(\varphi(\xi)\}\), respectively. Furthermore, the authors describe a method of the numerical solution of such inverse problems.