Exact Solutions > Linear Partial Differential Equations > Second-Order Parabolic Partial Differential Equations ## 1. Linear Parabolic Equations-
*w*_{t}=*aw*_{xx}. Heat equation (linear heat equation). -
*w*_{t}=*aw*_{xx}+ Φ(*x*,*t*). Nonhomogeneous heat equation. -
*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). -
*i**w*_{t}= −*kw*_{xx}+*U*(*x*)*w*. Schrodinger equation (linear Schrodinger equation).
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