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On the solution of reaction-diffusion equations with double diffusivity. (English) Zbl 0622.35036

The solution of a pair of coupled partial differential equations is derived. These equations arise in the solution of problems of flow of homogeneous liquids in fissured rocks and heat conduction involving two temperatures. These equations have been considered by Hill and Aifantis, but the technique we use appears to be simpler and more direct, and some new results are derived. Also, discussion about the propagation of initial discontinuities is given and illustrated with graphs of some special cases.

MSC:

35K57 Reaction-diffusion equations
35R05 PDEs with low regular coefficients and/or low regular data
35A22 Transform methods (e.g., integral transforms) applied to PDEs
76S05 Flows in porous media; filtration; seepage
80A20 Heat and mass transfer, heat flow (MSC2010)
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