Geodesic
Neumann Problem with the Integro-Differential Operator in the Boundary Condition
Matematičeskie zametki, Tome 100 (2016) no. 5, pp. 701-709

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The Neumann problem for a second-order parabolic equation with integro-differential operator in the boundary condition is considered. A well-posedness theorem is proved, in particular, the integral representation of the solution is obtained, estimates for the derivatives of the solution are established, and the kernel of the inverse operator of the problem is explicitly expressed.
Keywords: Neumann problem, second-order parabolic equation, integro-differential operator, Hölder space, Volterra–Fredholm integral equation of the second kind. 
@article{MZM_2016_100_5_a5,
     author = {I. M. Danyliuk and A. O. Danilyuk},
     title = {Neumann {Problem} with the {Integro-Differential} {Operator} in the {Boundary} {Condition}},
     journal = {Matemati\v{c}eskie zametki},
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     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2016_100_5_a5/}
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I. M. Danyliuk; A. O. Danilyuk. Neumann Problem with the Integro-Differential Operator in the Boundary Condition. Matematičeskie zametki, Tome 100 (2016) no. 5, pp. 701-709. http://geodesic.mathdoc.fr/item/MZM_2016_100_5_a5/