Consider the one$-$space dimensional heat equation for a temperature function T$($t$,$x$)$T$($t$,$x$),$ which is given by

$$tT$=$$2$xT$.$tT$=$$$x$2$T$.$

Select all the true statements below.

If you miss one correct answer, the problem will display all answers as incorrect.

A$.$ The boundary condition T$($t$,0)=0$T$($t$,0)=0$ means that the temperature of the system for all time is zero at x$=0$x$=0.$

B$.$ The boundary condition $$xT$($t$,$L$)=0$xT$($t$,$L$)=0$ means that the temperature of the system for all time is zero at x$=$Lx$=$L$.$

C$.$ The boundary condition T$($t$,0)=0$T$($t$,0)=0$ means that there is no heat flux entering or leaving the system for all times at x$=0$x$=0.$

D$.$ The one$-$space dimensional heat equation describes systems in three$-$dimesional space, where the temperature depends on only one space coordinate.

E$.$ The boundary condition $$xT$($t$,$L$)=0$xT$($t$,$L$)=0$ means that there is no heat flux entering or leaving the system for all times at x$=$Lx$=$L$.$

F$.$ The one$-$space dimensional heat equation describes only one$-$dimensional objects, which do not exist in nature, because objects in nature are three$-$dimensional.