Separation of Variables for Parabolic PDEs with Two Flux Boundary Conditions

6 Separation of Variables for Parabolic PDEs with Two Flux Boundary Conditions 

In section 7.1.5, non-homogeneity in the boundary conditions was removed by adding w(x) to the solution. However, for partial differential equations with two nonhomogeneous flux boundary conditions, this method does not work. [4] For this case two separate functions (w(x) v(t)) are introduced to take care of the nonhomogeneity of the boundary conditions and the separation of variables method is applied for the partial differential equation with the homogeneous boundary conditions. 

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