Hostname: page-component-669899f699-tzmfd Total loading time: 0 Render date: 2025-04-26T20:54:11.649Z Has data issue: false hasContentIssue false
  • English
  • Français

A reaction infiltration problem: classical solutions

Published online by Cambridge University Press:  20 January 2009

John Chadam ,
Xinfu Chen ,
Roberto Gianni  and
Riccardo Ricci
John Chadam
Affiliation:
Fields Institute for Research in the Mathematical Sciences, 185 Columbia Street, Waterloo, Ontario N2L 5Z5, Canada
Xinfu Chen
Affiliation:
Department of Mathematics, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, U.S.A.
Roberto Gianni
Affiliation:
Dipartimento di Matematica, Universita di Firenze, Florence, Italy
Riccardo Ricci
Affiliation:
Dipartimento di Matematica, Universita di Milano, Milan, Italy
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In this paper, we consider a reaction infiltration problem consisting of a parabolic equation for the concentration, an elliptic equation for the pressure, and an ordinary differential equation for the porosity. Existence and uniqueness of a global classical solution is proved for bounded domains Ω⊂RN, under suitable boundary conditions.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 40 , Issue 2 , June 1997 , pp. 275 - 291
Copyright
Copyright © Edinburgh Mathematical Society 1997

References

REFERENCES

1. Alt, H. W. and Dibenedetto, E.. Nonsteady flow of water and oil through inhomogeneous porous media, Ann. Scuola Norm. Sup. Pisa, IV 12 (1985), 335–392.Google Scholar
2. Campanato, S., Equazioni ellittiche del II ordine e spazi L(2,λ), Ann. Mat. Pura Appl. 69 (1965), 321–380.Google Scholar
3. Chadam, J., Chen, Xinfu, Comparini, E. and Ricci, R., Traveling wave solutions of a reaction-infiltration problem and a related free boundary problem, European J. Appl. Math., to appear.Google Scholar
4. Chadam, J., Chen, Xinfu, Gianni, R. and Ricci, R., A reaction infiltration problem: Existence, uniqueness, and regularity of solutions in two space dimensions, Math. Models Methods Appl. Sci., to appear.Google Scholar
5. Chadam, J., Hoff, D., Merino, E., Ortoleva, P. and Sen, A., Reactive Infiltration Instabilities, IMA J. Appl. Math. 36 (1987), 207–220.Google Scholar
6. Dibenedetto, E., in Theory and Applications of Liquid Cristal (IMA, Vol. 5), 123–141.Google Scholar
7. Gianni, R. and Ricci, R., Existence and Uniqueness for a Reaction-Diffusion Problem in Infiltration, Ann. Mat. Pura Appl., to appear.Google Scholar
8. Giaquinta, M., Multiple Integrals in the Calculus of Variations and Nonlinear Elliptic Systems (Princeton University Press, Princeton, New Jersey, 1983).Google Scholar
9. Gilbarg, G. and Trudinger, N. S., Elliptic Partial Differential Equations of Second Order (Springer, Berlin, 2nd ed., 1983).Google Scholar
10. Ladyženskaja, O. A., Solonnikov, V. A. and Ural'ceva, N. N., Linear and Quasilinear Equations of Parabolic Type (Translations of Mathematical Monographs, 23, Providence R.I., American Mathematical Society, 1968).Google Scholar
11. Ladyženskaja, O. A. and Ural'ceva, N. N., Equations aux dérivées partielles de type elliptique (Dunod, Paris, 1968).Google Scholar