Critical length for a linearly growing morphogen
= Critical length for a linearly growing morphogen
For $C_t=DC_{xx}+aC$ with $a>0$, $C(0,t)=0$, and $C_x(L,t)=0$, every mode decays exactly when
$$
L<\frac\pi2\sqrt{\frac Da}.
$$
= Critical length for a linearly growing morphogen
For $C_t=DC_{xx}+aC$ with $a>0$, $C(0,t)=0$, and $C_x(L,t)=0$, every mode decays exactly when
$$
L<\frac\pi2\sqrt{\frac Da}.
$$