Geodesic
A Nonstandard Cauchy Problem for the Heat Equation
Matematičeskie zametki, Tome 102 (2017) no. 2, pp. 270-283

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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
Mots-clés : Carleman formulas. 
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     title = {A {Nonstandard} {Cauchy} {Problem} for the {Heat} {Equation}},
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K. O. Makhmudov; O. I. Makhmudov; N. N. Tarkhanov. A Nonstandard Cauchy Problem for the Heat Equation. Matematičeskie zametki, Tome 102 (2017) no. 2, pp. 270-283. http://geodesic.mathdoc.fr/item/MZM_2017_102_2_a8/