On the behaviour of blow-up interfaces for an inhomogeneous filtration equation

IMA Journal of Applied Mathematics (Institute of Mathematics and Its Applications)

Volumn 57, Issue 1, 1996, Pages 53-77

  Galaktionov, V A ^a   King, J R ^b  

^a UNIVERSITY OF BATH   (United Kingdom)

^b UNIVERSITY OF NOTTINGHAM   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

ASYMPTOTIC STABILITY; CONVERGENCE OF NUMERICAL METHODS; INTERFACES (MATERIALS); MATHEMATICAL MODELS; PROBABILITY DENSITY FUNCTION;

BLOW UP INTERFACES; EXPONENTIAL DENSITY; FINITE TIME ASYMPTOTIC BEHAVIOUR; INHOMOGENEOUS FILTRATION EQUATION; ONE DIMENSIONAL; SELF SIMILAR SOLUTIONS;

NONLINEAR EQUATIONS;

EID: 0030205792     PISSN: 02724960     EISSN: None     Source Type: Journal    
DOI: 10.1093/imamat/57.1.53     Document Type: Article

References (20)

1. ANGENENT, S., 1988. The zero set of a solution of a parabolic equation. J. Reine Angew. Math. 390, 79-86.
2. ANGENENT, S. B., & ARONSON, D. G., 1996. The focusing problem for the radially symmetric porous medium equation. Commun. PDE. To appear.
3. ARONSON, D. G., & GRAVELEAU, J., 1993. A selfsimilar solution to the focusing problem for the porous medium equation. Eur. J. Appl. Math. 4, 65-81.
4. BARENBLATT, G. I., 1978. Similarity, Self-similarity, Intermediate Asymptotics. New York: Consultants Bureau.
5. GALAKTIONOV, V. A., 1995. On asymptotic self-similar behaviour for quasilinear heat equation: Single point blow-up, SIAM J. Math. Anal. 26, 675-93.
6. GALAKTIONOV, V. A., KAMIN, S., & KERSNER, R., 1996. On compactly supported solutions for nonlinear filtration equation in an inhomogeneous medium. To appear.
7. GALAKTIONOV, V. A., & PELETIER, L. A., 1996. Asymptotic behaviour near finite time extinction for the fast diffusion equation. To appear.
8. GALAKTIONOV, V. A., & VAZQUEZ, J. L., 1994. Extinction for a quasilinear heat equation with absorption I. Technique of intersection comparison. Commun. PDE 19, 1075-106.
9. GALAKTIONOV, V. A., & VAZQUEZ, J. L., 1995. Geometrical properties of the solutions of one-dimensional nonlinear parabolic equations. Math. Ann. 303, 741-69.
10. GRUNDY, R. E., 1993. Large time solution of an inhomogeneous nonlinear diffusion equation. Proc. R. Soc. Lond. A 286, 347-72.
11. KALASHNIKOV, A. S., 1987. Some problems of the qualitative theory of non-linear degenerate second-order parabolic equations. Uspekhi Matem. Nauk 42, 135-76 (in Russian). (English translation: 1987, Russian Math. Sun. 42, 169-222.)
12. KALASHNIKOV, A. S., 1987. Some problems of the qualitative theory of non-linear degenerate second-order parabolic equations. Uspekhi Matem. Nauk 42, 135-76 (in Russian). (English translation: 1987, Russian Math. Sun. 42, 169-222.)
13. KAMIN, S., & KERSNER, R., 1993. Disappearance of interfaces in finite time. Meccanica 28, 117-20.
14. KAMIN, S., & ROSENAU, P., 1981. Propagation of thermal waves in an inhomogeneous medium. Commun. Pure Appl. Math. 34, 831-52.
15. KAMIN, S., & ROSENAU, P., 1982. Non-linear diffusion in a finite mass medium. Commun. Pure Appl. Math. 35, 113-27.
16. KING, J. R., 1992. Local transformations between some nonlinear diffusion equations. J. Aust. Math. Soc. B 33, 321-49.
17. KING, J. R., 1993. Self-similar behaviour for the equation of fast nonlinear diffusion, Phil. Trans. R. Soc. Lond. A 343, 337-75.
18. KUNISCH, K., & PEICHL, G., 1988. On the shape of the solutions of second-order parabolic differential equations. J. Diff. Equat. 75, 329-53.
19. PELETIER, M. A., & ZHANG, H., 1994. Self-similar solutions of a fast diffusion equation that do not conserve mass, Report 94-40, Delft University of Technology.
20. SAMARSKII, A. A., GALAKTIONOV, V. A., KURDYUMOV, S. P., & MIKHAILOV, A. P., 1987. Blow-up in Quasilinear Parabolic Equations. Moscow: Nauka. (English translation: 1995, Berlin: Walter de Gruyter.)