Difference between revisions of "Delta heat equation"
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| − | Let $\mathbb{T}_1$ and $\mathbb{T}_2$ be [[time scale|time scales]]. Define the heat equation by | + | Let $\mathbb{T}_1$ and $\mathbb{T}_2$ be [[time scale|time scales]] and let $c \in \mathbb{R}$. Define the heat equation by |
$$u^{\Delta_1}=c^2 u^{\Delta_2^2},$$ | $$u^{\Delta_1}=c^2 u^{\Delta_2^2},$$ | ||
where $\Delta_1$ and $\Delta_2$ denote [[Partial Delta Derivative | partial $\Delta$-derivatives]]. | where $\Delta_1$ and $\Delta_2$ denote [[Partial Delta Derivative | partial $\Delta$-derivatives]]. | ||
| + | |||
| + | =References= | ||
| + | * {{PaperReference|Partial dynamic equations on time scales|2006|Billy Jackson||prev=|next=}}: Section 3.1 | ||
Latest revision as of 14:43, 15 January 2023
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
- Billy Jackson: Partial dynamic equations on time scales (2006): Section 3.1
