An inverse problem for a quasilinear parabolic equation with nonlocal boundary and overdetermination conditions

In this paper the inverse problem of finding the time-dependent coefficient of heat capacity together with the solution of heat equation with nonlocal boundary conditions is considered. Under some natural regularity and consistency conditions on the input data, the existence, uniqueness and continuous dependence upon the data of the solution are shown. Some considerations on the numerical solution for this inverse problem are presented with an example