Continuity of Weak Solutions to a General Porous Media Equation.
Technical summary rept.,
WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER
Pagination or Media Count:
The singular parabolic equations treated in this report serve as a model for filtration of fluids in porous media -- in particular, for the filtration of gases. The function serves as the model situation for such problems and makes the equation singular. Usually solutions of boundary value problems associated with such equations are found in a global sense, i.e. they are characterized as equivalence classes in certain Sobolev spaces. It is of interest to decide whether they may be defined pointwise and whether they possess some local regularity such as continuity. In this paper we prove that global weak solutions are in fact continuous. Moreover, we study under what circumstances their continuity can be extended up to the boundary of the domain where the process takes place.
- Numerical Mathematics
- Fluid Mechanics