ASYMPTOTIC PROFILES WITH FINITE MASS IN ONE-DIMENSIONAL CONTAMINANT TRANSPORT THROUGH POROUS MEDIA: THE FAST REACTION CASE

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Abstract
The paper considers the large-time behaviour of positive solutions of the equation with –∞t≥0, for pulse-type initial data. In suitably scaled variables this equation models the one-dimensional flow of a solute through a porous medium with the solute undergoing absorption by the solid matrix of the medium. With the total mass both absorbed and in solution invariant, it is shown that the asymptotic solution depends crucially on the value of p. For p>2 the solution approaches the symmetric solution of the linear heat equation centred on x=t, while for p=2 this becomes asymmetric due to the effect of nonlinearity. For 1<ppp≥2 the asymptotic solutions are uniformly valid in x but for 0<pp are compared with numerical solutions of the initial-value problem.

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