Small- and Waiting-Time Behavior of a Darcy Flow Model with a Dynamic Pressure Saturation Relation

@article{King2006SmallAW,
  title={Small- and Waiting-Time Behavior of a Darcy Flow Model with a Dynamic Pressure Saturation Relation},
  author={J. R. C. King and Carlota M. Cuesta},
  journal={SIAM Journal of Applied Mathematics},
  year={2006},
  volume={66},
  pages={1482-1511}
}
We address the small-time evolution of interfaces (fronts) for the pseudoparabolic generalization \[ {\partial u\over \partial t} = {\partial\over \partial x} \left( u^\alpha {\partial u\over \partial x} + u^\beta {\partial^2 u \over \partial x \partial t} \right) \] of the porous-medium equation, identifying regimes in which the local behavior remains fixed for some finite time and others in which it changes instantaneously. A number of phenomena beyond those exhibited by the porous-medium… CONTINUE READING

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