Abstract
In this chapter, we consider formulating the physical phenomena of heat conduction. We start with the derivation of the governing equation, the heat equation. This is followed by the introduction of the method of integral transform, a method typically used to solve PDE problems defined in infinitely large domains. We will also revisit the method of separation of variables, motivated by the need to find solutions for the initial–boundary value problems for the heat equation. Along this direction, the concept of the Sturm–Liouville differential equation system is then presented. In the end of this chapter, we discuss the maximum principle for the heat equation which underlies the diffusive feature of heat conduction. From a mathematical viewpoint, the maximum principle is presented to investigate the properties of solutions for problems governed by the heat equation.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2021 Science Press
About this chapter
Cite this chapter
Zhu, Y. (2021). The Heat Equation. In: Equations and Analytical Tools in Mathematical Physics. Springer, Singapore. https://doi.org/10.1007/978-981-16-5441-1_2
Download citation
DOI: https://doi.org/10.1007/978-981-16-5441-1_2
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-16-5440-4
Online ISBN: 978-981-16-5441-1
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)