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The Quarterly Journal of Mechanics and Applied Mathematics 1990 43(2):173-188; doi:10.1093/qjmam/43.2.173
© 1990 by Oxford University Press
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A MATHEMATICAL MODEL FOR ROCK BLASTING INVOLVING A DEGENERATE NONLINEAR DIFFUSION EQUATION

R. E. GRUNDY

( Department of Mathematical Sciences, University of St Andrews North Haugh, St Andrews KY16 9SS )

The nonlinear diffusion equation

has recently been proposed as a model describing the pressure distribution within fissures initiated by the blasting of rock. In this paper we look at the solution for a cylindrically symmetric charge together with the interaction of the pressure pulses emanating from two adjacent charges. In this latter situation it is necessary to examine similarity solutions of the equation. The uniqueness and existence of these solutions, as applied to the interaction problem, is discussed using a combination of numerical and analytic techniques.


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