## Linear Heat Equations-
*w*_{t}=*aw*_{xx}. Heat equation. -
*w*_{t}=*aw*_{xx}+ Φ(*x*,*t*). Heat equation with a source. -
*w*_{t}=*aw*_{xx}+*bw*_{x}+*cw*+ Φ(*x*,*t*). Convective heat equation with a source. -
*w*_{t}=*a*(*w*_{rr}+*r*^{−1}*w*_{r}). Heat equation with axial symmetry. -
*w*_{t}=*a*(*w*_{rr}+*r*^{−1}*w*_{r}) + Φ(*r*,*t*). Heat equation with axial symmetry (with a source). -
*w*_{t}=*a*(*w*_{rr}+ 2*r*^{−1}*w*_{r}). Heat equation with central symmetry. -
*w*_{t}=*a*(*w*_{rr}+ 2*r*^{−1}*w*_{r}) + Φ(*r*,*t*). Heat equation with central symmetry (with a source).
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