# Diffusion of fluid in a fissured medium with microstructure

@article{Showalter1991DiffusionOF, title={Diffusion of fluid in a fissured medium with microstructure}, author={R. E. Showalter and Noel J. Walkington}, journal={Siam Journal on Mathematical Analysis}, year={1991}, volume={22}, pages={1702-1722} }

A system of quasilinear degenerate parabolic equations arising in the modeling of diffusion in a fissured medium is studied. There is one such equation in the local cell coordinates at each point of the medium, and these are coupled through a similar equation in the global coordinates. It is shown that the initial boundary value problems are well posed in the appropriate spaces.

## 78 Citations

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## References

SHOWING 1-10 OF 26 REFERENCES

### Derivation of the double porosity model of single phase flow via homogenization theory

- Physics
- 1990

A general form of the double porosity model of single phase flow in a naturally fractured reservoir is derived from homogenization theory. The microscopic model consists of the usual equations…

### Kinetics of a Fixed Bed System for Solid Diffusion into Spherical Particles

- Engineering
- 1952

A solution is presented to the general problem of the transient behavior of a linear fixed bed system where the rate of adsorption is determined by the combined effect of a liquid film and solid…

### The Admittance Concept in the Kinetics of Chromatography

- Biology
- 1950

Experimental techniques for determining the kinetics of chromatographic processes with linear kinetics are indicated and a system admittance for the case where the influent concentration varies sinusoidally is obtained.