Difference between revisions of "Delta heat equation"

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$$u^{\Delta_1}=c^2 u^{\Delta_2^2},$$
 
$$u^{\Delta_1}=c^2 u^{\Delta_2^2},$$
 
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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[http://www.sciencedirect.com/science/article/pii/S0377042705001019 Partial dynamic equations on time scales]

Revision as of 21:26, 29 March 2015

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