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The Hölder Exponent for Radially Symmetric Solutions of Porous Medium Type Equations

Published online by Cambridge University Press:  20 November 2018

Gaston E. Hernandez  and
Ioannis M. Roussos
Gaston E. Hernandez
Affiliation:
Department of Mathematics University of Connecticut Storrs, Connecticut 06269-3009 USA
Ioannis M. Roussos
Affiliation:
Department of Mathematics Hamline University St. Paul, Minnesota 55104-1284 USA
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The density u(x, t) of an ideal gas flowing through a homogeneous porous media satisfies the equation Here m > 1 is a physical constant and u also satisfies the initial condition If the initial data is not strictly positive it is necessary to work with generalized solutions of the Cauchy problem (1), (2) (see [1]). By a weak solution we shall mean a function u(x, t) such that for (in the sense of distributions) and

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 43 , Issue 2 , 01 April 1991 , pp. 313 - 321
Copyright
Copyright © Canadian Mathematical Society 1991

References

1. Aronson, D.G., Regularity properties of flows through porous media: a counterexample, SIAM J. Appl. Math. 19(1970), 299–307.Google Scholar
2. Aronson, D.G., Regularity properties of gas through porous media, SIAM J. Appl. Math. 17(1969), 461–467.Google Scholar
3. Aronson, D.G. and Cafarelli, L.C., Optimal regularity for one dimensional porous medium, Revista Mat. Iberoamericana (4)2(1986), 357–366.Google Scholar
4. Benilam, P.N., A strong regularity if for solutions of the porous media equation, (in Contributions to Nonlinear Partial Differential Equations, Bardos, C. et al. editors), Research notes in Math, 89, Pitman, London, 1983, 39–58.Google Scholar
5. Caffarelli, L.A. and Friedman, A., Continuity of the density of a gas flow in a porous medium, Trans. Amer. Math. Soc. 252(1979), 99–113.Google Scholar
6. Caffarelli, L.A. and Friedman, A., Regularity of the free boundary of a gas flow in a n-dimensional porous medium, Indiana Univ. Math. J. 29(1980), 361–391.Google Scholar
7. Hernandez, G., the Hölder property in some degenerate parabolic problems, J. Diff. Eq. 65(1986), 240–249.Google Scholar
8. Sabinina, E.S., On the Cauchy problem for the equation of nonstationary gas filtration in several space variables, Dokl. Akad. Nauk SSSR 136(1961), 1034-1037.Google Scholar