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Mat. Zametki, 2017, Volume 102, Issue 2, Pages 270–283 (Mi mz11293)  

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.

Funding Agency Grant Number
German Academic Exchange Service (DAAD)
The research of the second author was supported by the Deutscher Akademischer Austauschdienst.


DOI: https://doi.org/10.4213/mzm11293

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English version:
Mathematical Notes, 2017, 102:2, 250–260

Bibliographic databases:

Document Type: Article
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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