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I don't understand where to even start with this problem. This book has ZERO examples. I would appreciate some help.

Show that by a suitable scaling of the space coordinates, the heat equation

[tex]u_{t}=\kappa\left(u_{xx}+u_{yy}+u_{zz}\right)[/tex]

can be reduced to the standard form

[tex]v_{t} = \Delta v [/tex] where u becomes v after scaling. [tex]\Delta [/tex] is the Laplacian operator

Show that by a suitable scaling of the space coordinates, the heat equation

[tex]u_{t}=\kappa\left(u_{xx}+u_{yy}+u_{zz}\right)[/tex]

can be reduced to the standard form

[tex]v_{t} = \Delta v [/tex] where u becomes v after scaling. [tex]\Delta [/tex] is the Laplacian operator

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