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Solution of the First Boundary‐Value Problem for a System of Autonomous Second‐Order Linear Partial Differential Equations of Parabolic Type with a Single Delay

Author

Listed:
  • Josef Diblík
  • Denis Khusainov
  • Oleksandra Kukharenko
  • Zdeněk Svoboda

Abstract

The first boundary‐value problem for an autonomous second‐order system of linear partial differential equations of parabolic type with a single delay is considered. Assuming that a decomposition of the given system into a system of independent scalar second‐order linear partial differential equations of parabolic type with a single delay is possible, an analytical solution to the problem is given in the form of formal series and the character of their convergence is discussed. A delayed exponential function is used in order to analytically solve auxiliary initial problems (arising when Fourier method is applied) for ordinary linear differential equations of the first order with a single delay.

Suggested Citation

  • Josef Diblík & Denis Khusainov & Oleksandra Kukharenko & Zdeněk Svoboda, 2012. "Solution of the First Boundary‐Value Problem for a System of Autonomous Second‐Order Linear Partial Differential Equations of Parabolic Type with a Single Delay," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    • Handle: RePEc:wly:jnlaaa:v:2012:y:2012:i:1:n:219040
    DOI: 10.1155/2012/219040
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    References listed on IDEAS

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    1. A. Boichuk & J. Diblík & D. Khusainov & M. Růžičková, 2011. "Boundary-Value Problems for Weakly Nonlinear Delay Differential Systems," Abstract and Applied Analysis, Hindawi, vol. 2011, pages 1-19, June.
    2. A. Boichuk & J. Diblík & D. Khusainov & M. Růžičková, 2011. "Boundary‐Value Problems for Weakly Nonlinear Delay Differential Systems," Abstract and Applied Analysis, John Wiley & Sons, vol. 2011(1).
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    Cited by:

    1. Jornet, Marc, 2021. "Exact solution to a multidimensional wave equation with delay," Applied Mathematics and Computation, Elsevier, vol. 409(C).
    2. Josef Diblík & Blanka Morávková, 2014. "Representation of the Solutions of Linear Discrete Systems with Constant Coefficients and Two Delays," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    3. Josef Diblík & Michal Fečkan & Michal Pospíšil, 2013. "Representation of a Solution of the Cauchy Problem for an Oscillating System with Multiple Delays and Pairwise Permutable Matrices," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).

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