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$L^p$ regularity of the solution of the heat equation with discontinuous coefficients
Selma Kouicema, Wided Chikoucheb a LMA, Department of Mathematics, Abderrahmane Mira University, Bejaia, Algeria
b LMPA, Department of Mathematics Mohamed Seddik Ben Yahia University, Jijel, Algeria
Abstract:
In this paper, we consider the transmission problem for the heat equation on a bounded plane sector in $L^{p}$-Sobolev spaces. By Applying the theory of the sums of operators of Da Prato-Grisvard and Dore-Venni, we prove that the solution can be splited into a regular part in $L^{p}$-Sobolev space and an explicit singular part.
Keywords:
transmission heat equation, sums of linear operators, singular behavior, non-smooth domains.
Received: 16.02.2020 Received in revised form: 23.04.2020 Accepted: 06.06.2020
Citation:
Selma Kouicem, Wided Chikouche, “$L^p$ regularity of the solution of the heat equation with discontinuous coefficients”, J. Sib. Fed. Univ. Math. Phys., 13:4 (2020), 466–479
Linking options:
https://www.mathnet.ru/eng/jsfu855 https://www.mathnet.ru/eng/jsfu/v13/i4/p466
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Abstract page: | 128 | Full-text PDF : | 74 | References: | 14 |
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