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.
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References
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Ebert, M.R., Reissig, M. (2018). Heat Equation—Properties of Solutions—Starting Point of Parabolic Theory. In: Methods for Partial Differential Equations. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-66456-9_9
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DOI: https://doi.org/10.1007/978-3-319-66456-9_9
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Publisher Name: Birkhäuser, Cham
Print ISBN: 978-3-319-66455-2
Online ISBN: 978-3-319-66456-9
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