Boundedness of Solutions to a Degenerate Diffusion Equation

  • Pavel KrejčíEmail author
Part of the Springer INdAM Series book series (SINDAMS, volume 22)


The diffusion equation with a bounded saturation range under the time derivative and with Robin boundary conditions is shown to admit a regular bounded solution provided that the saturation function and the permeability coefficient have controlled decay at infinity. The result remains valid even if Preisach hysteresis is present in the pressure-saturation relation. The method of proof is based on a Moser-Alikakos iteration scheme which is compatible with a generalized Preisach energy dissipation mechanism.


Degenerate parabolic equation Diffusion Hysteresis 

AMS (MOS) Subject Classification

35K65 47J40 


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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Institute of MathematicsAcademy of Sciences of the Czech RepublicPraha 1Czech Republic

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