 For example, Fisher's equation is a nonlinear PDE that includes the same diffusion term as the heat equation but incorporates a linear growth term and a nonlinear decay term.Under broad assumptions, an initial/boundary-value problem for a linear parabolic PDE has a solution for all time.The solution formula_11, as a function of formula_2 for a fixed time formula_38,
is generally smoother than the initial data formula_39.