Question

[&r, a1]7, that V2u = V.Vu = 6.4. Verify directly from the gradient operator that V ux+u-see Definition 6.5 Definition 6.5 (Two-Dimensional Heat or Diffusion Equation). Consider the open do- main (x,y) W. Using the continuity equation (1.4) the flux rule (6.13) yields DV u+R. (6.14) where V2u V.Vu u +lyy is the linear Laplacian operator The boundary conditions come in the three types: conditions on u, conditions on flux, and mixed as we are familiar with from Chapter 4. The region W is some open set, and the boundary is denoted aW. The conditions on u are termed Dirichlet boundary conditions:

Answer 1

ママu T T ] 'u [ ,2yJ (ahe)Q (U) + Prand Henee