Advertisement

Introduction

  • Ovidiu Calin
  • Der-Chen Chang
  • Kenro Furutani
  • Chisato Iwasaki
Chapter
Part of the Applied and Numerical Harmonic Analysis book series (ANHA)

Abstract

Consider the problem of finding the temperature of a gas contained in a volume V, which is supposed to be a bounded, open and connected set in ℝ3. Denote by u(x, t) the gas temperature at the point xV at time t. Let Ω be a subdomain of V with smooth boundary Ω. Let ν be the unit normal to Ω; see Fig. 1.1a. In order to write the equation of temperature evolution, we shall consider the law of conservation of thermal energy on the domain Ω, under the assumption that there is no external absorption or application of heat:

Keywords

Heat Equation Heat Kernel Eigenfunction Expansion Path Integral Method Eigenfunction Expansion Method 
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, LLC 2011

Authors and Affiliations

  • Ovidiu Calin
    • 1
  • Der-Chen Chang
    • 2
  • Kenro Furutani
    • 3
  • Chisato Iwasaki
    • 4
  1. 1.Department of MathematicsEastern Michigan UniversityYpsilantiUSA
  2. 2.Department of Mathematics and StatisticsGeorgetown UniversityWashingtonUSA
  3. 3.Department of Mathematics ScienceUniversity of TokyoNodaJapan
  4. 4.Department of Mathematical ScienceUniversity of HyogoHimejiJapan

Personalised recommendations