Abstract
(a) The initial-value problem The equation of heat for a function u=u(x1,...,x n ,t)=u(x,t) has the form
with a positive constant conductivity coefficient k. For n=3 the equation is satisfied by the temperature in a heat-conducting medium. For n=1 it holds for the temperature distribution in a heat-conducting insulated wire. The same type of equation occurs in the description of diffusion processes. Applying a suitable linear substitution on x,t we transform (1.1) into
which will be used in the discussion to follow.
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© 1978 Springer-Verlag New York Inc.
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John, F. (1978). Parabolic equations. In: Partial Differential Equations. Applied Mathematical Sciences, vol 1. Springer, New York, NY. https://doi.org/10.1007/978-1-4684-0059-5_7
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DOI: https://doi.org/10.1007/978-1-4684-0059-5_7
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