Delta heat equation

Let $\mathbb{T}_1$ and $\mathbb{T}_2$ be time scales and let $c \in \mathbb{R}$. Define the heat equation by $$u^{\Delta_1}=c^2 u^{\Delta_2^2},$$ where $\Delta_1$ and $\Delta_2$ denote partial $\Delta$-derivatives.

References

Partial dynamic equations on time scales