Question

Which of these are associated with a parabolic equation?

(a) Initial and boundary conditions

(b) Initial conditions only

(c) Boundary conditions only

(d) Neither initial conditions nor boundary conditions

I got this question in a job interview.

My query is from Mathematical Behaviour of PDE topic in chapter Mathematical Behaviour of Partial Differential Equations of Computational Fluid Dynamics

Answer 1

Right option is (a) Initial and boundary conditions

To explain I would say: Initial conditions come into the picture as parabolic equations are marching. This marching is done along the boundary conditions. Thus, both the initial conditions and boundary conditions are necessary for parabolic equations.