Geodesic
On initial boundary value problem for parabolic differential operator with non-coercive boundary conditions
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 13 (2020) no. 5, pp. 547-558

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We consider initial boundary value problem for uniformly $2$-parabolic differential operator of second order in cylinder domain in ${\mathbb R}^n $ with non-coercive boundary conditions. In this case there is a loss of smoothness of the solution in Sobolev type spaces compared with the coercive situation. Using by Faedo–Galerkin method we prove that problem has unique solution in special Bochner space.
Keywords: non-coercive problem, parabolic problem, Faedo–Galerkin method. 
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     author = {Alexander N. Polkovnikov},
     title = {On initial boundary value problem for parabolic differential operator with non-coercive boundary conditions},
     journal = {\v{Z}urnal Sibirskogo federalʹnogo universiteta. Matematika i fizika},
     pages = {547--558},
     publisher = {mathdoc},
     volume = {13},
     number = {5},
     year = {2020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JSFU_2020_13_5_a2/}
}
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Alexander N. Polkovnikov. On initial boundary value problem for parabolic differential operator with non-coercive boundary conditions. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 13 (2020) no. 5, pp. 547-558. http://geodesic.mathdoc.fr/item/JSFU_2020_13_5_a2/