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This article is cited in 2 scientific papers (total in 2 papers)
A Nonstandard Cauchy Problem for the Heat Equation
K. O. Makhmudova, O. I. Makhmudova, N. N. Tarkhanovb†
a A. Navoi Samarkand State University
b Universität Potsdam Institut für Mathematik
Abstract:
We consider the Cauchy problem for the heat equation in a cylinder $\mathcal{C}_T = \mathcal{X} \times (0,T)$ over a domain $\mathcal{X}$ in $\mathbb{R}^n$, with data on a strip lying on the lateral surface. The strip is of the form $S \times (0,T)$, where $S$ is an open subset of the boundary of $\mathcal{X}$. The problem is ill-posed. Under natural restrictions on the configuration of $S$, we derive an explicit formula for solutions of this problem.
Keywords:
heat equation, Cauchy problem, Carleman formulas.
† Author to whom correspondence should be addressed
DOI:
https://doi.org/10.4213/mzm11293
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English version:
Mathematical Notes, 2017, 102:2, 250–260
Bibliographic databases:
   
UDC:
517.95
Received: 28.06.2016
Revised: 19.11.2016
Citation:
K. O. Makhmudov, O. I. Makhmudov, N. N. Tarkhanov, “A Nonstandard Cauchy Problem for the Heat Equation”, Mat. Zametki, 102:2 (2017), 270–283; Math. Notes, 102:2 (2017), 250–260
Citation in format AMSBIB
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Linking options:
http://mi.mathnet.ru/eng/mz11293https://doi.org/10.4213/mzm11293 http://mi.mathnet.ru/eng/mz/v102/i2/p270
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