Solving a scalar degenerate multidimensional identification problem in a Banach space

We recover a non-negative time-dependent function, vanishing only at t = 0, in a linear multi-dimensional parabolic equation with a power degeneration. First we prove an existence and uniqueness result for an identification problem in a general Banach space via Semigroup Theory. Then we apply such a result to our specific linear parabolic equation related to a smooth bounded domain in ℝn.