The nonlocal conjugation problem for one-dimensional parabolic equation with discontinuous coefficients and associated Feller semigroup

B. I. Kopytko, R. V. Shevchuk
Theory of Stochastic Processes
Vol.24 (40), no.2, 2019, pp.17-31
By the boundary integral equations method we establish the classical solvability of the conjugation problem for one-dimensional linear parabolic equation of the second order (backward Kolmogorov equation) with nonlocal Feller-Wentzell conjugation condition. Using the solution of this problem, we construct the two-parameter Feller semigroup associated with the inhomogeneous diffusion process in bounded domain with moving membrane.