Positively invariant regions for a problem in phase transitions |
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Authors: | V Roytburd M Slemrod |
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Affiliation: | (1) Department of Mathematical Sciences, Rensselaer Polytechnic Institute, Troy, New York |
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Abstract: | Positively invariant regions for the system v
t
+ p(W)
x
= V
xx
, W
t
–V
x
= W
xx
are constructed where p < 0, w < , w > , p(w) = 0, w , > 0. Such a choice of p is motivated by the Maxwell construction for a van der Waals fluid. The method of an analysis is a modification of earlier ideas of Chueh, Conley, & Smoller 1]. The results given here provide independent L
bounds on the solution (w, v).Dedicated to Professor James Serrin on the occasion of his sixtieth birthday |
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Keywords: | |
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