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

In: Methods for Partial Differential Equations

Author

Listed:
  • Marcelo R. Ebert

    (University of São Paulo, Department of Computing and Mathematics)

  • Michael Reissig

    (TU Bergakademie Freiberg, Institute of Applied Analysis)

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.

Suggested Citation

  • Marcelo R. Ebert & Michael Reissig, 2018. "Heat Equation—Properties of Solutions—Starting Point of Parabolic Theory," Springer Books, in: Methods for Partial Differential Equations, chapter 0, pages 103-117, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-66456-9_9
    DOI: 10.1007/978-3-319-66456-9_9
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