Abstract:
The Cauchy problem is studied for a multidimensional difference equation in a class of functions defined at the integer points of a rational cone. We give an easy-to-check condition on the coefficients of the characteristic polynomial of the equation sufficient for solvability of the problem. A multidimensional analog of the condition ensuring stability of the Cauchy problem is stated on using the notion of amoeba of an algebraic hypersurface.
Keywords:
multidimensional difference equation, well-posedness of the Cauchy problem, rational cone.
The author was supported by the Government of the Russian Federation (Grant 14.Y26.31.0006) and the State Maintenance Program for the Leading Scientific Schools of the Russian Federation (Grant NSh-9149.2016.1.)
Citation:
T. I. Yakovleva, “Well-posedness of the Cauchy problem for multidimensional difference equations in rational cones”, Sibirsk. Mat. Zh., 58:2 (2017), 468–480; Siberian Math. J., 58:2 (2017), 363–372
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\paper Well-posedness of the Cauchy problem for multidimensional difference equations in rational cones
\jour Sibirsk. Mat. Zh.
\yr 2017
\vol 58
\issue 2
\pages 468--480
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\crossref{https://doi.org/10.17377/smzh.2017.58.218}
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\jour Siberian Math. J.
\yr 2017
\vol 58
\issue 2
\pages 363--372
\crossref{https://doi.org/10.1134/S0037446617020185}
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Linking options:
https://www.mathnet.ru/eng/smj2873
https://www.mathnet.ru/eng/smj/v58/i2/p468
This publication is cited in the following 6 articles:
Svetlana S. Akhtamova, Tom Cuchta, Alexander P. Lyapin, “An Approach to Multidimensional Discrete Generating Series”, Mathematics, 12:1 (2024), 143
Evgeny K. Leinartas, Tatiana I. Yakovleva, “Analytic solvability of the Hörmander problem and the Borel transformation of multiple Laurent series”, Zhurn. SFU. Ser. Matem. i fiz., 15:2 (2022), 186–195
E. K. Leinartas, T. I. Yakovleva, “Proizvodyaschaya funktsiya resheniya raznostnogo uravneniya i mnogogrannik Nyutona kharakteristicheskogo mnogochlena”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya Matematika, 40 (2022), 3–14
Alexander P. Lyapin, Sreelatha Chandragiri, “The Cauchy problem for multidimensional difference equations in lattice cones”, Zhurn. SFU. Ser. Matem. i fiz., 13:2 (2020), 187–196
Evgeny K. Leinartas, Tatiana I. Yakovleva, “The Cauchy problem for multidimensional difference equations and the preservation of the hierarchy of generating functions of its solutions”, Zhurn. SFU. Ser. Matem. i fiz., 11:6 (2018), 712–722
Evgeny K. Leinartas, Tatiana I. Yakovleva, “On formal solutions of the Hörmander’s initial-boundary value problem in the class of Laurent series”, Zhurn. SFU. Ser. Matem. i fiz., 11:3 (2018), 278–285
Citation in format AMSBIB
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