Boundary value problems
Barna A. Szabo, Ivo M. Babuska · 2021
In this chapter, the strong forms of boundary value problems are formulated from first principles with reference the problems of heat conduction in solid bodies and elasticity. The formulation of mathematical models for linear problems in heat conduction and elasticity is described in strong and generalized forms. The three-dimensional analogue of the model problem is the scalar elliptic boundary value problem. Steady state potential flow problems are among the physical phenomena that can be modeled as scalar elliptic boundary value problems. The chapter describes the formulation of a mathematical problem that models heat flow by conduction in solid bodies. Mathematical problems of linear elasticity belong in the category of vector elliptic boundary value problems. The unknown functions are the components of the displacement vector. There is a close analogy between the Stokes equations and the equations of incompressible elasticity.