Equilibrium Heat Distribution

  • Robert F. Brown

Abstract

The rest of Part I will be devoted to demonstrating the usefulness of two of the tools we have developed: a fixed point existence theorem (the Leray-Schauder alternative, a corollary of the Schauder theorem) and a compactness property of C k -spaces that is a consequence of the Ascoli-Arzela theorem. We used information from the Ascoli-Arzela and Schauder theories in Chapter 1, to prove the Cauchy-Peano theorem by topological methods. We will see a more recent application of these theories in the next chapter, in which we demonstrate the existence of solutions to a different type of problem in the theory of ordinary differential equations.

Keywords

Temperature Function Ordinary Differential Equa Topological Method Previous Chapter Ematical Condition 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer Science+Business Media New York 1993

Authors and Affiliations

  • Robert F. Brown
    • 1
  1. 1.Department of MathematicsUniversity of California, Los AngelesLos AngelesUSA

Personalised recommendations