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On Solutions to a Class of Functional Differential Equations with Time-Dependent Coefficients

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  • Muhammad Mohsin
  • Syed Touqeer H. Shah
  • Ali A. Zaidi
  • Wing-Sum Cheung

Abstract

In this paper, we study initial boundary value problems that involve functional (nonlocal) partial differential equations with variable coefficients. These problems arise in cell growth models with symmetric and asymmetric modes of division. We determine the general solution to the symmetric cell division problem for a certain class of coefficients and establish the convergence of solutions to a large time asymptotic solution. The existence of a steady size distribution (SSD) solution for an asymmetric cell division problem is established and is shown to be the large time-attracting solution for a certain class of coefficients. The rate of convergence of solutions towards the SSD solution is affected by the choice of coefficients and remains unaffected by the asymmetry in cell division. The uniqueness of solutions to the initial boundary value problem is also established.

Suggested Citation

  • Muhammad Mohsin & Syed Touqeer H. Shah & Ali A. Zaidi & Wing-Sum Cheung, 2022. "On Solutions to a Class of Functional Differential Equations with Time-Dependent Coefficients," Abstract and Applied Analysis, Hindawi, vol. 2022, pages 1-10, June.
    • Handle: RePEc:hin:jnlaaa:5849405
    DOI: 10.1155/2022/5849405
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