Finite time extinction in nonlinear diffusion equations

Applied Mathematics Letters

Volumn 17, Issue 5, 2004, Pages 561-567

  Laister, R ^a   Peplow, A T ^b   Beardmore, R E ^c  

^a UNIVERSITY OF THE WEST OF ENGLAND   (United Kingdom)

^b ROYAL INSTITUTE OF TECHNOLOGY   (Sweden)

^c IMPERIAL COLLEGE LONDON   (United Kingdom)

Author keywords

Degenerate diffusion; Extinction; Finite travelling waves; Singular

Indexed keywords

COMPUTER SIMULATION; DATA REDUCTION; DIFFUSION; MATHEMATICAL OPERATORS; MATHEMATICAL TECHNIQUES; PROBLEM SOLVING; SIGNAL PROCESSING; VELOCITY MEASUREMENT;

DEGENERATE DIFFUSION; EXTINCTION; FINITE TRAVELLING WAVES (FTW); SINGULAR;

NONLINEAR EQUATIONS;

EID: 2442688981     PISSN: 08939659     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0893-9659(04)90126-7     Document Type: Article

References (11)

1. D.G. Aronson and H.F. Weinberger, Nonlinear diffusion in population genetics and nerve pulse propagation, In Partial Differential Equations and Related Topics, Lecture Notes in Mathematics, Volume 446, (Edited by J.A. Goldstein), pp. 45-49, Springer-Verlag, New York, (1975).
2. P.C. Fife and J.B. McLeod, The approach of solutions of nonlinear diffusion equations to travelling front solutions, Arch. Rat. Mech. Anal. 65, 335-361, (1977).
3. Ya.I. Kanel', Stabilization of solutions of equations of combustion theory for initial functions of compact support, Mat. Sbornik 65 (3), 398-413, (1964).
4. F. Sanchez-Garduno and P.K. Maini, Travelling wave phenomena in some degenerate reaction-diffusion equations, J. Differential Equations 117, 281-319, (1995).
5. Y. Hosono, Travelling wave solutions for some density dependent diffusion equations, Japan J. Appl. Math. 3, 163-196, (1986).
6. A.A. Samarskii, V.A. Galaktionov, S.P. Kurdyumov and A.P. Mikhailov, Blow-up in quasilinear parabolic equations, In de Gruyter Expositions in Mathematics, Volume 19, Walter de Gruyter, Berlin, (1995).
7. G. Reyes and A. Tesei, Basic theory for a diffusion-absorption equation in an inhomogeneous medium, Non. Diff. Eqns. Appl. 10 (2), 197-222, (2003).
8. D.G. Aronson, Density-dependent interaction-diffusion systems, In Dynamics and Modelling of Reactive Systems, (Edited by W.E. Steward, W.H. Ray and C.C. Conley), pp. 161-176, Academic Press, (1980).
9. H. Engler, Relations between travelling wave solutions of quasilinear parabolic equations, Proc. Amer. Math. Soc. 93 (2), 297-302, (1985).
10. J. Carr, Applications of centre manifold theory, In Applied Mathematical Sciences, Volume 35, Springer-Verlag, New York, (1981).
11. R. Kersner, Degenerate parabolic equations with general nonlinearities, Nonlinear Anal. Theory Methods Appl. 4 (6), 1043-1062, (1980).