How long does it take for a gas to fill a porous container?

Authors:
Carmen Cortázar and Manuel Elgueta

Journal:
Proc. Amer. Math. Soc. **122** (1994), 449-453

MSC:
Primary 35K65; Secondary 76S05

DOI:
https://doi.org/10.1090/S0002-9939-1994-1232138-0

MathSciNet review:
1232138

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Abstract: Let us consider the problem for for , and for . Here we assume , and . It is well known that solutions to this problem have the property of finite speed propagation of the perturbations. By this we mean that if *z* is an interior point of *D* and exterior to the support of , then there exists a time so that for and for . In this note we give, in an elementary way, an upper bound for for the case of bounded convex domains and in the case of a half space.

**[A]**D. G. Aronson,*Nonlinear diffusion problems*, Free Boundary Problems: Theory and Applications (A. Fasano and M. Primicerio, eds.), Pitman, New York, 1983, pp. 135-149. MR**714914 (85g:76023)****[AC]**D. G. Aronson and L. A. Caffarelli,*The initial trace of the solution of the porous medium equation*, Trans. Amer. Math. Soc.**280**(1983), 351-366. MR**712265 (85c:35042)****[CF]**L. A. Caffarelli and A. Friedman,*Regularity of the free boundary of a gas flow in an n-dimensional porous medium*, Indiana. Univ. Math. J.**29**(1980), 361-391. MR**570687 (82a:35096)****[CVW]**L. A. Caffarelli, J. L. Vazquez, and N. I. Wolanski,*Lipschitz continuity of solutions and interfaces of the N-dimensional porous medium equation*, Indiana Univ. Math. J.**36**(1987), 373-401. MR**891781 (88k:35221)**

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DOI:
https://doi.org/10.1090/S0002-9939-1994-1232138-0

Keywords:
Diffusion,
porous media

Article copyright:
© Copyright 1994
American Mathematical Society