Question Number 202094 by otchereabdullai@gmail.com last updated on 20/Dec/23
$$\:{A}\:{computer}\:{systerm}\:{has}\:{a}\:{memory}\: \\ $$$$\:\:{leak}\:{issue}\:{causing}\:{its}\:{usage}\:{to} \\ $$$$\:\:{increase}\:{over}\:{time}.\:{the}\:{rate}\:{of}\: \\ $$$$\:\:{memory}\:{usage}\:{growth}\:{is}\:{directly}\: \\ $$$$\:\:{proportional}\:{to}\:{the}\:{difference}\: \\ $$$$\:\:{between}\:{the}\:{current}\:{memory}\:{usage}\: \\ $$$$\:{and}\:{the}\:{systerms}\:{maximum}\:{memory} \\ $$$$\:\:{capacity}.\:{Write}\:{one}\:{ODE}\:{and}\:{one}\: \\ $$$$\:\:{PDE}\:{that}\:{models}\:{the}\:{memory}\:{usage} \\ $$$$\:\:{growth}. \\ $$
Commented by mr W last updated on 20/Dec/23
$${C}={maximum}\:{memory}\:{capacity} \\ $$$${M}={current}\:{memory}\:{usage} \\ $$$${the}\:{ODE}\:{is}: \\ $$$$\frac{{dM}}{{dt}}={k}\left({C}−{M}\right) \\ $$$${a}\:{PDE}\:{doesn}'{t}\:{exist},\:{because}\:{M}\: \\ $$$${only}\:{depends}\:{on}\:{one}\:{variable},\:{the} \\ $$$${time}\:{t}. \\ $$
Commented by otchereabdullai@gmail.com last updated on 20/Dec/23
$${Thank}\:{you}\:{prof}\:{W} \\ $$