Hi all. Let $a$ and $b$ be two real variables such that $0 \le a \le a_{max}$ and $0 \le b \le b_{max}$. I must write the following if-then-else condition with linear inequalities:

if $a < a_{max}$ then $b = 0$ else $b \ge 0$.

Is it possible by adding a single binary variable $y$?