How to prove two partial different equations are dual

Question

I have $m(t, x)$ and $n(t, x)$, where $t \geq 0$ is the time variable and $x \in \mathbb{R}$ is the space variable. I also have a speed $x \mapsto v(x)$. We consider the following models: $$ \frac{\partial m}{\partial t}(t, x)+v(x) \frac{\partial m}{\partial x}(t, x)=0, \quad \frac{\partial n}{\partial t}(t, x)+\frac{\partial}{\partial x}[v(x) n(t, x)]=0 $$ Actually, with the initial condition, i can find an explicit formula for $m$ and $n$. But, i also have a task which is "Prove these two partial differential equations are dual". I don't know how to do it. I try to find the definition of two dual partial differential equations on the Internet but i don't receive a result. Can you help me to solve this problem. This is the first time i have had a chance to study this field. Any help is appreciated.