In solving an equation, I used a method of variable substitution. Do you think this method is a typical or popular one?
In[189]:= (*equation*)
In[190]:= eq1 = D[c[r, t], t] == 1/r*D[r*D[c[r, t], r], r]
Out[190]=
\!\(\*SuperscriptBox[\(c\), \*
TagBox[
RowBox[{"(",
RowBox[{"0", ",", "1"}], ")"}],
Derivative],
MultilineFunction->None]\)[r, t] == (
\!\(\*SuperscriptBox[\(c\), \*
TagBox[
RowBox[{"(",
RowBox[{"1", ",", "0"}], ")"}],
Derivative],
MultilineFunction->None]\)[r, t] + r
\!\(\*SuperscriptBox[\(c\), \*
TagBox[
RowBox[{"(",
RowBox[{"2", ",", "0"}], ")"}],
Derivative],
MultilineFunction->None]\)[r, t])/r
(*variable substitution at infinity, \
r->R/\[Sigma],t->\[Tau]/(\[Sigma]^2).*)
In[196]:= eq5 =
eq1 /. {c -> (c1[#1*\[Sigma], #2*\[Sigma]^2] &),
r -> (#1/\[Sigma] &[R, \[Tau]]),
t -> (#2/\[Sigma]^2 &[R, \[Tau]])} // Simplify // Normal
Out[196]= \[Sigma] (
\!\(\*SuperscriptBox[\(c1\), \*
TagBox[
RowBox[{"(",
RowBox[{"0", ",", "1"}], ")"}],
Derivative],
MultilineFunction->None]\)[R, \[Tau]] - (
\!\(\*SuperscriptBox[\(c1\), \*
TagBox[
RowBox[{"(",
RowBox[{"1", ",", "0"}], ")"}],
Derivative],
MultilineFunction->None]\)[R, \[Tau]] + R
\!\(\*SuperscriptBox[\(c1\), \*
TagBox[
RowBox[{"(",
RowBox[{"2", ",", "0"}], ")"}],
Derivative],
MultilineFunction->None]\)[R, \[Tau]])/R) == 0