On a class of parabolic equations with variable density and absorption

Advances in Differential Equations

Volumn 7, Issue 2, 2002, Pages 155-176

  Kersner, Robert ^a   Reyes, Guillermo ^b   Tesei, Alberto ^b  

^a INSTITUTE OF EXPERIMENTAL MEDICINE   (Hungary)

^b SAPIENZA UNIVERSITY OF ROME   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0141741774     PISSN: 10799389     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (16)

1. M. Bertsch, A class of degenerate diffusion equations with a singular nonlinear term, Nonlinear Anal. 7 (1983), 117-127.
2. M. Bertsch, R. Kersner and L.A. Peletier, Positivity versus localization in a degenerate diffusion equation, Nonlinear Anal. 9 (1985), 987-1008.
3. X.-Y. Chen, H. Matano and M. Mimura, Finite-point extinction and continuity of interfaces in a nonlinear diffusion equation with strong absorption, J. Reine Angew. Math. 459 (1995), 1-36.
4. D. Eidus, The Cauchy problem for the nonlinear filtration equation in an inhomogeneous medium, J. Differential Equations 84 (1990), 309-318.
5. V. Galaktionov and J.R. King, On behaviour of blow-up interfaces for an inhomogeneous filtration equation, IMA J. Appl. Math. 57 (1996), 53-77.
6. V.A. Galaktionov, S. Kamin and R. Kersner, On compactly supported solutions to nonlinear filtration equations in an inhomogeneous medium (unpublished manuscript, 1993).
7. M. Guedda, D. Hilhorst and M.A. Peletier, Disappearing interfaces in nonlinear diffusion, Adv. Math. Sci. Appl. 7 (1997), 695-710.
8. A.S. Kalashnikov, Some problems of the qualitative theory of non-linear degenerate second-order parabolic equations, Usp. Mat. Nauk 42 (1987), 135-176. English translation in: Russian Math. Surveys 42 (1987), 169-222.
9. S. Kamin, Heat propagation in an inhomogeneous medium. In: Progress in Partial Differential Equations: the Metz Surveys 4, 229-237 (Pitman Research Notes Math. Ser. 345; Longman, Harlow, 1996).
10. S. Kamin and R. Kersner, Disappearence of interfaces in finite time, Meccanica 28 (1993), 117-120.
11. S. Kamin and P. Rosenau, Propagation of thermal waves in an inhomogeneous medium, Comm. Pure Appl. Math. 34 (1981), 831-852.
12. S. Kamin and P. Rosenau, Nonlinear diffusion in a finite mass medium, Comm. Pure Appl. Math. 35 (1982), 113-127.
13. M.A. Peletier, A supersolution for the porous media equation with nonuniform density, Appl. Math. Lett. 7 (1994), 29-32.
14. L.A. Peletier and A. Tesei, Diffusion in inhomogeneous media: localization and positivity, Ann. Mat. Pura Appl. 141 (1985), 307-330.
15. L.A. Peletier and A. Tesei, Global bifurcation and attractivity of stationary solutions of a degenerate diffusion equation, Adv. Appl. Math. 7 (1986), 435-454.
16. G. Reyes and A. Tesei, Basic theory for a diffusion-absorption equation in an inhomogeneous medium (in preparation).