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does anyone know the general solution to the 2d heat equation, namely
subject to
if anyone could help me I'd be well chuffed!
Taken directly from David Colton's book - ifOriginally Posted by raheel88
hello all.
does anyone know the general solution to the 2d heat equation, namely
subject to
if anyone could help me I'd be well chuffed!is continuous and bounded in absolute then the solution is
![<br />
u(x_1,x_2,\tau) = \frac{1}{4 \pi \tau} \int_{-\infty}^{\infty} \int_{-\infty}^{\infty} u_0({\xi}_1,{\xi}_2)\, \text{exp} \left[ - \frac{(x_1-{\xi}_1)^2+(x_2-{\xi}_2)^2}{4 \tau} \right] d {\xi}_1 d {\xi}_2<br />](http://latex.codecogs.com/png.latex? <br />
u(x_1,x_2,\tau) = \frac{1}{4 \pi \tau} \int_{-\infty}^{\infty} \int_{-\infty}^{\infty} u_0({\xi}_1,{\xi}_2)\, \text{exp} \left[ - \frac{(x_1-{\xi}_1)^2+(x_2-{\xi}_2)^2}{4 \tau} \right] d {\xi}_1 d {\xi}_2<br />
)
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