Inverse Source Problem for a Singular Parabolic Equation with Variable Coefficients

We consider a parabolic equation with a singular potential in a bounded domain Ω⊂Rn. The main result is a Lipschitz stability estimate for an inverse source problem of determining a spatial varying factor f(x) of the source term R(x,t)f(x). We obtain a consistent stability result for any μ≤p1μ*, where p1>0 is the lower bound of p(x) and μ*=(n−2)2/4, and this condition for μ is also almost a consistently optimal condition for the existence of solutions. The main method we used is the Carleman estimate, and the proof for the inverse source problem relies on the Bukhgeim–Klibanov method.