Geodesic
On the first initial-boundary-value problem of heat conduction in a domain with curvilinear lateral boundaries
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh spring mathematical school "Modern methods of the theory of boundary-value problems. Pontryagin readings – XXXI". Voronezh, May 3-9, 2020, Tome 204 (2022), pp. 146-159

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We consider the first initial-boundary-value problem for the heat equation in a bounded domain $\Omega$ with curvilinear lateral boundaries. Using the method of boundary integral equations, we prove the existence of a solution to this problem in the class $C^{2,1}_{x,t}(\overline{\Omega})$.
Keywords: first initial-boundary-value problem, nonsmooth lateral boundary, method of boundary integral equations.
Mots-clés : parabolic equation 
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     author = {K. D. Fedorov},
     title = {On the first initial-boundary-value problem of heat conduction in a domain with curvilinear lateral boundaries},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {146--159},
     publisher = {mathdoc},
     volume = {204},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2022_204_a14/}
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K. D. Fedorov. On the first initial-boundary-value problem of heat conduction in a domain with curvilinear lateral boundaries. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh spring mathematical school "Modern methods of the theory of boundary-value problems. Pontryagin readings – XXXI". Voronezh, May 3-9, 2020, Tome 204 (2022), pp. 146-159. http://geodesic.mathdoc.fr/item/INTO_2022_204_a14/