Geodesic
The nonlocal conjugation problem for one-dimensional parabolic equation with discontinuous coefficients and associated Feller semigroup
Teoriâ slučajnyh processov, Tome 24 (2019) no. 2, pp. 17-31

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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.
Keywords: Feller semigroup, parabolic potential, method of successive approximations. 
@article{THSP_2019_24_2_a2,
     author = {B. I. Kopytko and R. V. Shevchuk},
     title = {The nonlocal conjugation problem for one-dimensional parabolic equation with discontinuous coefficients and associated {Feller} semigroup},
     journal = {Teori\^a slu\v{c}ajnyh processov},
     pages = {17--31},
     publisher = {mathdoc},
     volume = {24},
     number = {2},
     year = {2019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/THSP_2019_24_2_a2/}
}
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B. I. Kopytko; R. V. Shevchuk. The nonlocal conjugation problem for one-dimensional parabolic equation with discontinuous coefficients and associated Feller semigroup. Teoriâ slučajnyh processov, Tome 24 (2019) no. 2, pp. 17-31. http://geodesic.mathdoc.fr/item/THSP_2019_24_2_a2/