Аннотация:We study statements of nolinear problems for a parabolic equation with an unknown coefficient at the time derivative. One of the statements is a system, which contains the boundary value problem of the first kind and the equation for a time dependence of the sought coefficient.
In the other statements the corresponding system is distinguished by boundary conditions. For these nonlinear systems, conditions of unique solvability in a class of smooth functions are proved by applying the Rothe method and a priori estimates in the difference-continuous analogs of Holder spaces. The present investigation is connected with the mathematical modelling of physical-chemical processes in which inner properties of materials are subjected to changes.