The interfaces of one-dimensional flows in porous media

Author:
Juan L. Vázquez

Journal:
Trans. Amer. Math. Soc. **285** (1984), 717-737

MSC:
Primary 35R35; Secondary 76S05

MathSciNet review:
752500

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Abstract: The solutions of the equation for , where is a nonnegative Borel measure that vanishes for (and satisfies a growth condition at ), exhibit a finite, monotone, continuous interface that bounds to the right the region where . We perform a detailed study of : initial behaviour, waiting time, behaviour as . For certain initial data the solutions blow up in a finite time : we calculate in terms of and describe the behaviour of as .

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1984-0752500-8

Keywords:
Flows in porous media,
interfaces,
blow-up time,
waiting time,
asymptotic behaviour

Article copyright:
© Copyright 1984
American Mathematical Society