A uniqueness theorem for a class of non-classical parabolic equations
Hong‐Ming Yin · Applicable Analysis · 1989
In this paper we deal with a general non-classical parabolic equation in which a certain functional of the solution with respect to one of its arguments is involved as the coefficients of the equation. This system of equations is representative of a large class of inverse problems with a equation of parabolic type and an unknown parameter p = p(t). We prove an important lemma which improves the known weak singularity estimate for the Green's function of a linear parabolic boundary value problem. The uniqueness is demonstrated by virtue of a perturbation argument applied in conjunction with the results of Lemma and a generalized Gronwall-Bellman's inequality.