A model of the process of salt and moisture transfer is investigated. This model is described by the equation \[ \frac{\partial u}{\partial t}-\sum_{i,j=1}^{n} \frac{\partial}{\partial x_{i}}\left(a_{ij} \left(x;\varphi_{ij}^{(1)}\right)\frac{\partial u}{\partial x_{j}}\right) +\sum_{i=1}^{n}b_{i} \left(x;\varphi_{i}^{(2)}\right)\frac{\partial u}{\partial x_{i}} + c\left(x;\varphi^{(3)}\right)u=f(t,x;\varphi^{(4)}), \] \[ u|_{t=0}=0,\quad u|_{x\in\partial\Omega}=0, \] where \(u=u(t,x)\) is a function which describe the system in a region \(Q=[0,T]\times\Omega,\) and \(\Omega\subset{\mathbb{R}}^{n}\) is a bounded set with a smooth bound \(\partial\Omega.\) The problem is to find an admissible control \(\varphi=\left(\varphi_{ij}^{(1)}, \varphi_{i}^{(2)},\varphi^{(3)},\varphi^{(4)}\right)\) which gives a minimum to a functional \(J(\varphi).\) An analogue of the Galerkin method is proposed for the solution of the problem.