Geodesic
On solvability of conjugation problems with non-ideal contact conditions
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 7 (2020), pp. 18-32

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In the article we examine the questions of regular solvability in the Sobolev spaces of the transmission problems with transmission conditions of non-ideal contact type for parabolic second order systems. A solution has all generalized derivatives occurring in the system summable to some power $p\in (1,\infty)$. At the interface the limit values of the conormal derivatives are expressed trough the limit values of a solution. The problem does not belong to the class of classical diffraction problems and arises when describing heat-and-mass transfer processes. The proof relies on a priori bounds and the method of continuation in a parameter.
Mots-clés : transmission problem
Keywords: discontinuous coefficient, parabolic system, heat-and-mass transfer. 
@article{IVM_2020_7_a2,
     author = {V. A. Belonogov and S. G. Pyatkov},
     title = {On solvability of conjugation problems with non-ideal contact conditions},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {18--32},
     publisher = {mathdoc},
     number = {7},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2020_7_a2/}
}
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V. A. Belonogov; S. G. Pyatkov. On solvability of conjugation problems with non-ideal contact conditions. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 7 (2020), pp. 18-32. http://geodesic.mathdoc.fr/item/IVM_2020_7_a2/