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Nonlocal Problems for the Fourth Order Impulsive Partial Differential Equations

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Differential and Difference Equations with Applications (ICDDEA 2019)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 333))

Abstract

Nonlocal problems for an impulsive system of fourth-order partial differential equations are investigated. By the method of introducing additional functions, the problems under study are reduced to an equivalent problem consisting of the impulsive system of second-order hyperbolic equations and integral relations. Algorithm for finding the approximate solutions to the equivalent problem is constructed and its convergence is proved. Sufficient conditions are obtained for the unique solvability of a nonlocal problem for the impulsive system of fourth-order partial differential equations. As an example, the conditions for the unique solvability of a periodic problem for the impulsive system of fourth-order partial differential equations are established.

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Acknowledgements

One of the article authors (Assanova) has participated at the International Conference on Differential & Difference Equations and Applications 2019 in Lisbon.

We sincerely thank Prof. Sandra Pinelas, the Chair of the conference, for the excellent organization of ICDDEA-2019.

Researches presented in the article are supported by the grant of the Ministry of Education and Science of the Republic of Kazakhstan, Project No. AP 05131220, for 2018–2020 years.

The authors thank the referees for his/her careful reading of the manuscript and useful suggestions which allowed us to improve the present paper.

Author information

Authors and Affiliations

  1. Institute of Mathematics and Mathematical Modeling, 125 Pushkin str., A26G7T5, Almaty, Kazakhstan

    Anar T. Assanova, Aziza D. Abildayeva & Agila B. Tleulessova

  2. L.N. Gumilyov Eurasian National University, 13 Kazhymukhan str., Z01C0X0, Nur-Sultan, Kazakhstan

    Agila B. Tleulessova

Authors
  1. Anar T. Assanova
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  2. Aziza D. Abildayeva
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  3. Agila B. Tleulessova
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Corresponding author

Correspondence to Anar T. Assanova .

Editor information

Editors and Affiliations

  1. Department of Exact Sciences and Engineering, Military Academy, Lisbon, Portugal

    Sandra Pinelas

  2. Department of Mathematics, University of Tennessee at Chattanooga, Chattanooga, TN, USA

    John R. Graef

  3. Mathematik und Didaktik, Katholische Universität Eichstätt, Eichstätt, Bayern, Germany

    Stefan Hilger

  4. Huazhong University of Science and Technology, Wuhan, Hubei, China

    Peter Kloeden

  5. Department of Electrical and Computer Engineering, Democritus University of Thrace, Xanthi, Xanthi, Greece

    Christos Schinas

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Assanova, A.T., Abildayeva, A.D., Tleulessova, A.B. (2020). Nonlocal Problems for the Fourth Order Impulsive Partial Differential Equations. In: Pinelas, S., Graef, J.R., Hilger, S., Kloeden, P., Schinas, C. (eds) Differential and Difference Equations with Applications. ICDDEA 2019. Springer Proceedings in Mathematics & Statistics, vol 333. Springer, Cham. https://doi.org/10.1007/978-3-030-56323-3_7

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