C Infinity-Regularity for the Porous Median Equation.
Technical summary rept.,
WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER
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The equation stated in the abstract describes the expansion of a gas in a one dimensional porous medium. While existence of weak solutions can be obtained by standard energy methods, not much was known about regularity of the solution near the free boundaries. The difficulty is that the equation degenerates at the boundary and the hyperbolic term becomes dominant. The authors show in this report that despite of the degeneracy the free boundary is smooth with the possible exception of a discontinuity in the derivative at the waiting time. Their method is based on energy estimates in weighted norms using some of the ideas in another document. Additional keywords estimates, approximationmathematics finite difference theory finite element analysis.
- Fluid Mechanics