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  
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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]].
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=References=
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* {{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