Heat Equation—Properties of Solutions—Starting Point of Parabolic Theory

Marcelo R. Ebert and Michael Reissig
Additional contact information
Marcelo R. Ebert: University of São Paulo, Department of Computing and Mathematics
Michael Reissig: TU Bergakademie Freiberg, Institute of Applied Analysis

Chapter Chapter 9 in Methods for Partial Differential Equations, 2018, pp 103-117 from Springer

Abstract: Abstract There exists comprehensive literature on the theory of parabolic partial differential equations. One of the simplest parabolic partial differential equation is the heat equation. By means of this equation we explain qualitative properties of solutions as maximum-minimum principle, non-reversibility in time, infinite speed of propagation and smoothing effect. Moreover, we explain connections to thermal potential theory. Thermal potentials prepare the way for integral equations for densities in single- or double-layer potentials as solutions to mixed problems.

Date: 2018
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-66456-9_9

Ordering information: This item can be ordered from
http://www.springer.com/9783319664569

DOI: 10.1007/978-3-319-66456-9_9

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().