Some inverse problems for mathematical models of heat and mass transfer

In the article we consider well-posedness questions of inverse problems for mathematical models of heat and mass transfer. We recover a solution of a parabolic equation of the second order and a coefficient in this equation characterizing parameters of a medium and belonging to the kernel of a differential operator of the first order with the use of data of the first boundary value problem and the additional Neumann condition on the lateral boundary of a cylinder (thereby we have the Cauchy data on the lateral boundary of a cylinder). An unknown coefficient can occur in the main part of the equation. A solution is sought in a Sobolev space with sufficiently large summability exponent and an unknown coefficient in the class of continuous functions. The problem is shown to have a unique stable solution locally in time.