On Nonlinear Initial Boundary Value Problems of Heat Conduction and Diffusion
K. A. Zischka, Pao-Liu Chow · SIAM Review · 1974
Heat conduction and diffusion problems are frequently encountered by physicists and engineers in various fields of applications. This paper treats the nonlinear case of the heat conduction and diffusion equation in both its theoretical and practical aspects. In the theoretical part of the paper, a nonlinear heat conduction equation is derived under quite general assumptions, and it is shown that well-known particular forms of the equation can be derived from the general form under certain simplifying assumptions. The commonly encountered initial boundary value conditions are enunciated and some special forms of the problem formulated. Existence and uniqueness theorems are stated and proved briefly. The practical part of the paper shows the development, which lags that of the theory, of approximate methods suitable for numerical applications and the restrictions to which these methods are subject.