On existence and uniqueness of solutions to a pantograph type equation
Keywords:hyperbolic partial differential equations, funtional partial differential equations, Cauchy problems
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.