DefinitionThe classification of PDEs involves identification of the properties of these equations: rank, linearity, order, and coefficients. Based on their characteristics, and on the properties of their solutions, PDEs can be grouped into such types as elliptic, parabolic, and hyperbolic. Classification of PDEs is helpful to suggest appropriate methods of solution as well as give the physical interpretation of PDEs. PDEs describe the behavior of systems in physics, engineering, and mathematical modeling. Solution: ∂t∂u=k∇2u (Heat equation) (Parabolic PDE describing the diffusion of heat over time) The parabolic classification of The boundary-value problem indicates that its solutions are governed by initial conditions, as opposed to boundary conditions.
