Determination of a coefficient in a quasilinear parabolic equation with periodic boundary condition

In this paper, we consider the problem of determining the time-dependent thermal diffusivity and the temperature distribution in one-dimensional quasilinear heat equation with periodic boundary and integral overdetermination conditions. We establish conditions for the existence, uniqueness and continuous dependent of a classical solution of the problem under considerations. We present some results on the numerical solution with two examples.

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