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This article is cited in 1 scientific paper (total in 1 paper)
Global in space regularity results for the heat equation with Robin–Neumann type boundary conditions in time-varying domains
Tahir Boudjeriou, Arezki Kheloufi Bejaia University, Bejaia, 6000, Algeria
Abstract:
This article deals with the heat equation $$ \partial _{t}u-\partial _{x}^{2} u=f\; \text{in}\; D,\; D =\left\{ \left( t,x\right) \in \mathbb{R}^{2}:a<t<b,\psi \left( t\right) <x<+\infty\right\} $$ with the function $\psi$ satisfying some conditions and the problem is supplemented with boundary conditions of Robin-Neumann type. We study the global regularity problem in a suitable parabolic Sobolev space. We prove in particular that for $f\in L^{2}(D)$ there exists a unique solution $u$ such that $u,\; \partial_{t}u,\; \partial_{x}^{j}u\in L^{2}\left( D\right),j=1,\;2.$ The proof is based on the domain decomposition method. This work complements the results obtained in [10].
Keywords:
heat equation, unbounded non-cylindrical domains, Robin condition, Neumann condition, anisotropic Sobolev spaces.
Received: 27.04.2018 Received in revised form: 18.01.2019 Accepted: 06.03.2019
Citation:
Tahir Boudjeriou, Arezki Kheloufi, “Global in space regularity results for the heat equation with Robin–Neumann type boundary conditions in time-varying domains”, J. Sib. Fed. Univ. Math. Phys., 12:3 (2019), 355–370
Linking options:
https://www.mathnet.ru/eng/jsfu760 https://www.mathnet.ru/eng/jsfu/v12/i3/p355
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