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The asymptotic behaviour of the heat equation in a twisted Dirichlet-Neumann waveguide
- 1.0367928 - ÚJF 2013 RIV US eng J - Journal Article
Krejčiřík, David - Zuazua, E.
The asymptotic behaviour of the heat equation in a twisted Dirichlet-Neumann waveguide.
Journal of Differential Equations. Roč. 250, č. 5 (2011), s. 2334-2346. ISSN 0022-0396. E-ISSN 1090-2732
R&D Projects: GA MŠMT LC06002
Institutional research plan: CEZ:AV0Z10480505
Keywords : Laplacian * Dirichlet and Neumann boundary conditions * Twist
Subject RIV: BE - Theoretical Physics
Impact factor: 1.277, year: 2011
We consider the heat equation in a straight strip, subject to a combination of Dirichlet and Neumann boundary conditions. We show that a switch of the respective boundary conditions leads to an improvement of the decay rate of the heat semigroup of the order of t(-1/2). The proof employs similarity variables that lead to a non-autonomous parabolic equation in a thin strip contracting to the real line, that can be analysed on weighted Sobolev spaces in which the operators under consideration have discrete spectra.
Permanent Link: http://hdl.handle.net/11104/0202435
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