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Time-Variable Extension of the Solution of a Nonlocal Multipoint Problem for Partial Differential Equations with Constant Coefficients

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Abstract

A problem with nonlocal multipoint conditions for the nth-order partial differential equation with constant coefficients is considered. In the case where conditions of strict averaging of time intervals are specified, the existence of a solution of the problem in a cylinder that is the Cartesian product of a time interval and a p-dimensional spatial torus is discussed. It is found that under certain conditions of separability of the roots of the characteristic equation for almost all (in the sense of the Lebesgue measure) coefficients of the equation and parameters of the conditions, the solution of the problem cannot be extended in the time variable beyond the extreme points at which the conditions are given.

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References

  1. V. S. Ilkiv, “Investigation of the region of existence of a solution of a nonlocal problem, ” in: Proceedings of the Xth Conference of Young Scientists of the Institute of Applied Problems of Mechanics and Mathematics of the Academy of Sciences of the UkSSR, Part 2 [in Russian] (Lviv, 15–17 May, 1984), (the manuscript was deposited at the VINITI 10.11.1984, No 7197–84 Dep), Lviv (1984), pp. 100–108.

  2. V. S. Ilkiv, “A multipoint nonlocal problem for partial differential equations with constant coeficients, ” in: Proceedings of the IXth Conference of Young Scientists of the Institute of Applied Problems of Mechanics and Mathematics of the Academy of Sciences of the UkSSR [in Russian] (Lviv, 10–14 May, 1982), (manuscript deposited at VINITI 10.01.1984, No 324–84 Dep), Lviv (1983), pp. 64–72.

  3. S. Mizohata, The Theory of Partial Differential Equations, Cambridge University Press, Cambridge (1973).

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  4. B. I. Ptashnik, Incorrect Boundary-Value Problems for Partial Differential Equations [in Russian], Naukova Dumka, Kyiv (1984).

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Authors and Affiliations

  1. State University “Lviv Polytechnics”, Ukraine

    V. S. Ilkiv

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  1. V. S. Ilkiv
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Ilkiv, V.S. Time-Variable Extension of the Solution of a Nonlocal Multipoint Problem for Partial Differential Equations with Constant Coefficients. Journal of Mathematical Sciences 107, 3615–3619 (2001). https://doi.org/10.1023/A:1011954509838

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  • DOI: https://doi.org/10.1023/A:1011954509838

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