On Existence and Uniqueness of Solutions to a Pantograph Type Equation

Mohsin, Muhammad; Zaidi, Ali Ashher

doi:10.1017/s144618112100002x

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2022

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“…The full problem, even for constant coefficients, has not been solved hitherto. Recently, the existence of a unique solution to the problem for constant coefficients has been established [16].…”

Section: Introductionmentioning

confidence: 99%

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

Mohsin

Shah

Zaidi

2022

Abstract and Applied Analysis

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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.

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Section: Introductionmentioning

confidence: 99%