Geodesic
On the solution to a two-dimensional heat conduction problem in a degenerate domain
Eurasian mathematical journal, Tome 11 (2020) no. 3, pp. 89-94

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In a degenerate domain, namely, the inverted cone, we consider a boundary value problem of heat conduction. For this problem the solvability theorems are established in weighted spaces of essentially bounded functions. The proofs of the theorems are based on the results of the solvability for a nonhomogeneous integral equation of the third kind. The problem under study is reduced to the study of this integral equation using the representation of the solution to the boundary value problem in the form of a sum of constructed thermal potentials. 
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     author = {M. T. Jenaliyev and M. I. Ramazanov and M. T. Kosmakova and Zh. M. Tuleutaeva},
     title = {On the solution to a two-dimensional heat conduction problem in a degenerate domain},
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     url = {http://geodesic.mathdoc.fr/item/EMJ_2020_11_3_a7/}
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M. T. Jenaliyev; M. I. Ramazanov; M. T. Kosmakova; Zh. M. Tuleutaeva. On the solution to a two-dimensional heat conduction problem in a degenerate domain. Eurasian mathematical journal, Tome 11 (2020) no. 3, pp. 89-94. http://geodesic.mathdoc.fr/item/EMJ_2020_11_3_a7/