On existence and uniqueness of solutions to a pantograph type equation

Muhammad Mohsin; Ali Ashher  Zaidi

doi:10.21914/anziamj.v62.15885

Authors

Muhammad Mohsin Lahore University of Management Sciences https://orcid.org/0000-0002-1037-3842
Ali Ashher Zaidi Lahore University of Management Sciences https://orcid.org/0000-0002-6961-3804

DOI:

https://doi.org/10.21914/anziamj.v62.15885

Keywords:

hyperbolic partial differential equations, funtional partial differential equations, Cauchy problems

Abstract

We show existence and uniqueness of solutions to an initial boundary value problem that entails a pantograph type functional partial differential equation with two advanced nonlocal terms. The problem models cell growth and division into two daughter cells of different sizes. There is a paucity of information about the solution to the problem for an arbitrary initial cell distribution.

doi:10.1017/S144618112100002X

Author Biographies

Muhammad Mohsin, Lahore University of Management Sciences

Department of Mathematics, Lahore University of Management Sciences, Lahore, Pakistan

Ali Ashher Zaidi, Lahore University of Management Sciences