The interfaces of one-dimensional flows in porous media
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- by Juan L. Vázquez PDF
- Trans. Amer. Math. Soc. 285 (1984), 717-737 Request permission
Abstract:
The solutions of the equation ${u_t} = {({u^m})_{x x}}$ for $x \in {\mathbf {R}},0 < t < T,m > 1$, where $u(x,0)$ is a nonnegative Borel measure that vanishes for $x > 0$ (and satisfies a growth condition at $- \infty$), exhibit a finite, monotone, continuous interface $x = \zeta (t)$ that bounds to the right the region where $u > 0$. We perform a detailed study of $\zeta$: initial behaviour, waiting time, behaviour as $t \to \infty$. For certain initial data the solutions blow up in a finite time ${T^{\ast }}$: we calculate ${T^{\ast }}$ in terms of $u(x,0)$ and describe the behaviour of $\zeta$ as $t \uparrow {T^{\ast }}$.References
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Additional Information
- © Copyright 1984 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 285 (1984), 717-737
- MSC: Primary 35R35; Secondary 76S05
- DOI: https://doi.org/10.1090/S0002-9947-1984-0752500-8
- MathSciNet review: 752500