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Nonlocal Problem for a System of Partial Differential Equations of Higher Order with Pulsed Actions

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Ukrainian Mathematical Journal Aims and scope

We consider a nonlocal problem for a system of partial differential equations of higher order with pulsed actions. By introducing new unknown functions, the analyzed problem is reduced to an equivalent problem including a nonlocal problem for the impulsive system of the second-order hyperbolic equations and integral relations. We propose an algorithm for finding the solutions of the equivalent problem based on the solution of the nonlocal problem for the system of hyperbolic equations of the second order with pulsed action for fixed values of the introduced additional functions, which are then determined from the integral relations in terms of the obtained solution. Sufficient conditions for the existence of unique solution of the nonlocal problem for an impulsive system of hyperbolic equations of the second order are obtained by method of introduction of functional parameters. The algorithms for finding its solutions are constructed. Conditions for the unique solvability of the nonlocal problem for a system of partial differential equations of higher order with pulsed actions are established in terms of the coefficients of the system and boundary matrices.

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Authors and Affiliations

  1. Institute of Mathematics and Mathematical Modelling, Almaty, Kazakhstan

    A. T. Assanova

  2. Institute of Mathematics and Mathematical Modelling, Almaty, Gumilev Eurasian National University, Astana, Kazakhstan

    A. B. Tleulessova

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  1. A. T. Assanova
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  2. A. B. Tleulessova
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Correspondence to A. T. Assanova.

Additional information

Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 71, No. 12, pp. 1587–1606, December, 2019.

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Assanova, A.T., Tleulessova, A.B. Nonlocal Problem for a System of Partial Differential Equations of Higher Order with Pulsed Actions. Ukr Math J 71, 1821–1842 (2020). https://doi.org/10.1007/s11253-020-01750-9

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  • DOI: https://doi.org/10.1007/s11253-020-01750-9

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