On Solutions to a Class of Functional Differential Equations with Time-Dependent Coefficients
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 di...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2022-01-01
|
| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2022/5849405 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832553665946189824 |
|---|---|
| author | Muhammad Mohsin Syed Touqeer H. Shah Ali A. Zaidi |
| author_facet | Muhammad Mohsin Syed Touqeer H. Shah Ali A. Zaidi |
| author_sort | Muhammad Mohsin |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-227a53411f5547a591086018ec4a5dd7 |
| institution | Kabale University |
| issn | 1687-0409 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-227a53411f5547a591086018ec4a5dd72025-02-03T05:53:29ZengWileyAbstract and Applied Analysis1687-04092022-01-01202210.1155/2022/5849405On Solutions to a Class of Functional Differential Equations with Time-Dependent CoefficientsMuhammad Mohsin0Syed Touqeer H. Shah1Ali A. Zaidi2Department of MathematicsDepartment of MathematicsDepartment of MathematicsIn 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.http://dx.doi.org/10.1155/2022/5849405 |
| spellingShingle | Muhammad Mohsin Syed Touqeer H. Shah Ali A. Zaidi On Solutions to a Class of Functional Differential Equations with Time-Dependent Coefficients Abstract and Applied Analysis |
| title | On Solutions to a Class of Functional Differential Equations with Time-Dependent Coefficients |
| title_full | On Solutions to a Class of Functional Differential Equations with Time-Dependent Coefficients |
| title_fullStr | On Solutions to a Class of Functional Differential Equations with Time-Dependent Coefficients |
| title_full_unstemmed | On Solutions to a Class of Functional Differential Equations with Time-Dependent Coefficients |
| title_short | On Solutions to a Class of Functional Differential Equations with Time-Dependent Coefficients |
| title_sort | on solutions to a class of functional differential equations with time dependent coefficients |
| url | http://dx.doi.org/10.1155/2022/5849405 |
| work_keys_str_mv | AT muhammadmohsin onsolutionstoaclassoffunctionaldifferentialequationswithtimedependentcoefficients AT syedtouqeerhshah onsolutionstoaclassoffunctionaldifferentialequationswithtimedependentcoefficients AT aliazaidi onsolutionstoaclassoffunctionaldifferentialequationswithtimedependentcoefficients |