Determination of a diffusion coefficient in a quasilinear parabolic equation
This paper investigates the inverse problem of finding the time-dependent diffusion coefficient in a quasilinear parabolic equation with the nonlocal boundary and integral overdetermination conditions. Under some natural regularity and consistency conditions on the input data the existence uniqueness and continuously dependence upon the data of the solution are shown. Finally some numerical experiments are presented.
Nonlocal boundary condition
Integral overdetermination condition
Time-dependent diffusion coefficient