A Half-Inverse Problem for the Coefficients of a Diffusion Equation
Yang Chuanfu · Chinese Annals of Mathematics · 2011
Generally speaking,the coefficients q(x) and p(x) in a diffusion operator can be uniquely determined by two spectra or one spectrum and norming constants.In this paper, by using the Hochstadt and Lieberman's method,it is shown that(a) if p(x) is prescribed on the interval[π/2,π]and q(x) is full given on[0,π],then a single spectrum suffices to determine p(x) on[0,π/2];(b) if q(x) is prescribed on the interval[π/2,π]and p(x) is full given on[0,π], then a single spectrum suffices to determine q(x) on[0,π/2].