Hyperbolic phenomena in a strongly degenerate parabolic equation |
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Authors: | Michiel Bertsch Roberta Dal Passo |
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Institution: | (1) Dipartimento di Matematica II, Universitá di Roma Tor Vergata , Via Fontanile di Carcaricola, 00133 Rome;(2) Istituto per le Applicazioni del Calcolo, Viale del Policlinico 137, 00161 Rome |
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Abstract: | We consider the equation u
t
=( (u) (u
x
))
x
, where >0 and where is a strictly increasing function with lim
s![rarr](/content/mv2ugn5j4r8064m4/xxlarge8594.gif)
=
< . We solve the associated Cauchy problem for an increasing initial function, and discuss to what extent the solution behaves qualitatively like solutions of the first-order conservation law u
t
=
( (u))
x
. Equations of this type arise, for example, in the theory of phase transitions where the corresponding free-energy functional has a linear growth rate with respect to the gradient. |
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Keywords: | |
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