Accurate computation of traveling wave solutions of some nonlinear diffusion equations

Wave Motion

Volumn 44, Issue 3, 2007, Pages 222-230

  Mansour, M B A ^a  

^a SOUTH VALLEY UNIVERSITY   (Egypt)

Author keywords

35A20; 35A40; 35K65; Degenerate diffusion; Singular nonlinear Nagumo equations; Traveling wave solutions

Indexed keywords

BOUNDARY VALUE PROBLEMS; COMPUTATIONAL METHODS; NONLINEAR EQUATIONS; PARTIAL DIFFERENTIAL EQUATIONS; PROBLEM SOLVING;

DEGENERATE DIFFUSION; NONLINEAR DIFFUSION EQUATIONS; SINGULAR NONLINEAR NAGUMO EQUATIONS; TRAVELING WAVE EQUATIONS; TRAVELING WAVE SOLUTIONS;

WAVE EQUATIONS;

BOUNDARY VALUE PROBLEMS; COMPUTATIONAL METHODS; NONLINEAR EQUATIONS; PARTIAL DIFFERENTIAL EQUATIONS; PROBLEM SOLVING; WAVE EQUATIONS;

DIFFUSION; NONLINEARITY; NUMERICAL METHOD; TRAVEL TIME; WAVE VELOCITY;

EID: 33845782137     PISSN: 01652125     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.wavemoti.2006.10.001     Document Type: Article

References (11)

1. Aronson D.G., and Weinberger H.F. Nonlinear Diffusion in Population Genetics, Combustion and Nerve Propagation, Partial Differential Equations and Related Topics. Lecture Notes in Mathematics vol. 446 (1975), Springer, Berlin
2. Gurtin M.E., and MacCamy R.C. On the diffusion of biological populations. Math. Biosci. 33 (1977) 35-49
3. Hosono Y. Travelling wave solutions for some density dependent diffusion equations. Jpn. J. Appl. Math. 3 (1986) 163-196
4. Murray J.D. Mathematical Biology (1989), Springer, Berlin, Heidelberg, New York
5. Grindrod P., and Sleeman B.D. Weak travelling fronts for population models with density-dependent diffusion. Math. Meth. Appl. Sci. 9 (1987) 576-586
6. Garduño F.S., and Maini P.K. Travelling wave phenomena in non-linear diffusion degenerate Nagumo equations. J. Math. Biol. 35 (1997) 713-728
7. M.B.A. Mansour, Singularity Analysis for Travelling Wave Solutions of Degenerate Diffusion and Transport Equations Modelling Cell Motility, Ph.D. Thesis, University of Bonn 2001.
8. Carr J. Applications of Centre Manifold Theory (1981), Springer, Berlin, Heidelberg, New York
9. Atkinson C., Reuter G.E.H., and Ridler-Rowe C.J. Traveling wave solutions for some nonlinear diffusion equations. SIAM J. Math. Anal. 6 (1981) 880-892
10. Press H.W., Flannery B.P., Teukolsky S.A., and Vetterling W.T. Numerical Recipes (1986), Cambridge University Press, London/New York
11. Crank J. Free and Moving Boundary Problems (1988), Oxford University Press, Oxford