Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



Interaction of gas fronts

Authors: A. A. Lacey and J. L. Vázquez
Journal: Quart. Appl. Math. 50 (1992), 469-478
MSC: Primary 76L05; Secondary 76N15
DOI: https://doi.org/10.1090/qam/1178428
MathSciNet review: MR1178428
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Abstract: During rock blasting separate charges initiate movement of gas at high pressure through fractured rock. This gas occupies regions of compact support enclosed by moving boundaries, the gas fronts, at which the pressure is effectively zero. Here we consider the local behaviour of such gas fronts, albeit taking the system to be rather simpler so that the gas flow can be modelled by the porous medium equation, when two identically pressurized regions interact and when a gas front impinges upon a fixed boundary where the pressure is zero.

References [Enhancements On Off] (What's this?)

  • [1] G. I. Barenblatt, On the self-similar solutions of the Cauchy problem for nonlinear parabolic equation of nonstationary filtration, Prikl. Math. Mech. 20, 761-763 (1956) MR 0086580
  • [2] H. E. Erhie, D. Phil. thesis, Oxford University, 1988
  • [3] J. R. Esteban and J. L. Vazquez, Homogeneous diffusion in $ \mathbb{R}$ with power like nonlinear diffusivity, Arch. Rat. Mech. Anal. 103, 39-80 (1988) MR 946969
  • [4] R. E. Grundy, A mathematical model for rock blasting involving a degenerate nonlinear diffusion equation, Quart J. Mech. Appl. Math. 43, 173-188 (1990) MR 1059002
  • [5] R. E. Pattle, Diffusion from an instantaneous point source with concentration dependent coefficient, Quart J. Mech. Appl. Math. 12, 407-409 (1959) MR 0114505

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DOI: https://doi.org/10.1090/qam/1178428
Article copyright: © Copyright 1992 American Mathematical Society

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