Motivation and Framework

摘要: It is not difficult to motivate, from a practical point of view, the kind situations we would like deal with and analyze. We have selected typical example in heat conduction, but many other examples are as valid this one. Suppose two very different materials at our disposal: first, conductivity α1 = 1, good expensive conductor; cheap material, almost an insulator coefficient α0 0. 001. These be used fill up given design domain Q, which assume unit square for simplicity (Fig. 1.1), proportions t1, t0, t1 + t0 1. Typically, < that first material much more than second. will take, definiteness, 4, 6. The thermal device isolated all over ∂ except small sink Γ0 middle left side where normalize temperature vanish, there uniform source Q size unity. mixture decided so dissipated energy possible.