35K05 Heat equation
35K10 General theory of second-order, parabolic equations
35K15 Initial value problems for second-order, parabolic equations
35K20 Boundary value problems for second-order, parabolic equations 
35K25 General theory of higher-order, parabolic equations
35K30 Initial value problems for higher-order, parabolic equations
35K35 Boundary value problems for higher-order, parabolic equations
35K40 General theory of parabolic systems of PDE
35K45 Initial value problems for parabolic systems
35K50 Boundary value problems for parabolic systems
35K55 Nonlinear PDE of parabolic type
35K57 Reaction-diffusion equations
35K60 Nonlinear boundary value problems for linear parabolic PDE; boundary value problems for nonlinear parabolic PDE
35K65 Parabolic partial differential equations of degenerate type
35K70 Ultraparabolic, pseudoparabolic PDE, etc.
35K85 Unilateral problems and variational inequalities for parabolic PDE [See also 35R35, 49J40]
35K90 Abstract parabolic evolution equations
35K99 None of the above, but in this section