The initial trace of a solution of the porous medium equation

Authors:
D. G. Aronson and L. A. Caffarelli

Journal:
Trans. Amer. Math. Soc. **280** (1983), 351-366

MSC:
Primary 35K55; Secondary 76S05

MathSciNet review:
712265

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Abstract: Let be a continuous weak solution of the porous medium equation in for some . We show that corresponding to there is a unique nonnegative Borel measure on which is the initial trace of . Moreover, we show that the initial trace must belong to a certain growth class. Roughly speaking, this growth restriction shows that there are no solutions of the porous medium equation whose pressure grows, on average, more rapidly then as .

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DOI:
https://doi.org/10.1090/S0002-9947-1983-0712265-1

Article copyright:
© Copyright 1983
American Mathematical Society