4. Variational formulation for various one-dimensional PDEs

When the elasticity model problem was put into variational form, it was transformed into an equivalent problem, with both problems admitting the same solution. The weak formulation apparently does not include any boundary conditions; these are in fact included in the choice of the space $H_0^1\left(\left[0,\mathrm{\hspace{0.17em}}1\right]\right)$ of test functions associated with the problem under consideration. As mentioned above, the approach is general and involves, after choosing the space E of test functions according to the problem under consideration, multiplying the partial differential equation by a function of E and integrating...