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Nonlocal Problem with Impulsive Action for Parabolic Equations of the Vector Order

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Ukrainian Mathematical Journal Aims and scope

For \( \left\{\overset{\sim }{p};\overrightarrow{h}\right\} \)-parabolic equations with continuous coefficients, we study the problem of finding classical solutions satisfying modified initial conditions with generalized data in the form of Gelfand- and Shilovtype distributions. This condition linearly combines the values of the solution at the initial time and at a certain intermediate time point. We establish the conditions for the correct solvability of this problem and deduce the formula for its solution. By using the obtained results, we solve the corresponding problem with impulsive action.

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Authors and Affiliations

  1. Yu. Fed’kovych Chernivtsi National University, Chernivtsi, Ukraine

    G. M. Unguryan

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  1. G. M. Unguryan
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Correspondence to G. M. Unguryan.

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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 73, No. 11, pp. 1532–1540, November, 2021. Ukrainian DOI: https://doi.org/10.37863/umzh.v73i11.6521.

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Unguryan, G.M. Nonlocal Problem with Impulsive Action for Parabolic Equations of the Vector Order. Ukr Math J 73, 1772–1782 (2022). https://doi.org/10.1007/s11253-022-02029-x

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