Precise computations of chemotactic collapse using moving mesh methods

Journal of Computational Physics

Volumn 202, Issue 2, 2005, Pages 463-487

  Budd, C J ^a   Carretero Gonzalez R ^b   Russell, R D ^c  

^a University of Bath   (United Kingdom)

^b SAN DIEGO STATE UNIVERSITY   (United States)

^c SIMON FRASER UNIVERSITY   (Canada)

Author keywords

Adaptive mesh methods; Blow up; Chemotaxis; Collapse

Indexed keywords

BIOCHEMISTRY;

ADAPTIVE MESH METHOD; BLOW-UP; BLOWUP SOLUTIONS; CHEMOTACTIC COLLAPSE; CHEMOTAXI; COLLAPSE; DYNAMIC SCALE; MOVING MESH METHOD; SELF-SIMILAR; SPATIAL DIMENSION;

MESH GENERATION;

EID: 10244229064     PISSN: 00219991     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jcp.2004.07.010     Document Type: Article

References (32)

1. M.D. Betterton M.P. Brenner Collapsing bacterial cylinders Phys. Rev. E 64 2001 61904
2. M.A. Herrero J.J.L. Velázquez Singularity patterns in a chemotaxis model Math. Ann. 306 1996 583-623
3. E.F. Keller L.A. Segel Initiation of slime mold aggregation viewed as an instability J. Theo. Biol. 6 1970 399-415
4. E.F. Keller L.A. Segel Model for chemotaxis J. Theo. Biol. 26 1971 225-234
5. E.F. Keller L.A. Segel Traveling bands of chemotactic bacteria: A theoretical analysis J. Theo. Biol. 30 1971 235-248
6. M.P. Brenner, T.P. Witelski, On Spherically Symmetric Gravitational Collapse, preprint, 1998
7. P. Biler, T. Nadzieja, Global and exploding solutions in a model of self-gravitating systems, preprint
8. T. Hanawa K. Nakayama Stability of similarity solutions for a gravitationally contracting isothermal sphere: Convergence to the Larson Penston solution The Astrophys. J. 484 1997 238-244
9. I.A. Guerra, Stabilization and Blow-up for some Multidimensional Nonlinear PDEs, PhD Thesis, TU Eindhoven, 2003
10. H.A. Levine B.D. Sleeman A system of reaction diffusion equations arising in the theory of reinforced random walks SIAM J. Appl. Math. 57 3 1997 683-730
11. J.J.L. Velázquez Stability of some mechanisms of chemotactic aggregation SIAM J. Appl. Math. 62 5 2002 1581-1633
12. C.J. Budd W. Huang R.D. Russell Moving mesh methods for problems with blow-up SIAM J. Sci. Comput. 17 2 1996 305-327
13. W. Huang R.D. Russell A moving collocation method for the numerical solution of time dependent partial differential equations Appl. Numer. Math. 20 1996 101-116
14. W. Huang Y. Ren R.D. Russell Moving mesh partial differential equations based on the equidistribution principle SIAM J. Numer. Anal. 31 1994 709-730
15. W. Huang Y. Ren R.D. Russell Moving mesh methods based on moving mesh partial differential equations J. Comput. Phys. 113 1994 279-290
16. C.J. Budd, R.D. Russell, in preparation
17. H.G. Othmer A. Stevens Aggregation, blowup, and collapse: The ABC's of t-axis in reinforced random walks SIAM J. Appl. Math. 57 4 1997 1044-1081
18. W. Jäger S. Luckhaus On explosions of solutions to a system of partial differential equations modelling chemotaxis Trans. Amer. Math. Soc. 329 1992 819-824
19. T. Nagai Behavior of solutions to a parabolic-elliptic system modelling chemotaxis J. Korean Math. Soc. 37 2000 721-733
20. T. Nagai Blowup of nonradial solutions to parabolic-elliptic systems modelling chemotaxis in two-dimensional domains J. Inequal. Appl. 6 2001 37-55
21. C.-S. Lin W.-M. Ni I. Takagi Large amplitude stationary solutions to a chemotaxis system J. Diff. Eq. 72 1988 1-27
22. W.-M. Ni Diffusion, cross-diffusion, and their spike layer steady states Notices Amer. Math. Soc. 45 1998 9-18
23. M.A. Herrero E. Medina J.J.L. Velázquez Finite-time aggregation into a single point in a reaction-diffusion system Nonlinearity 10 1997 1739-1754
24. M.A. Herrero E. Medina J.J.L. Velázquez Self-similar blow-up for a reaction diffusion-system J. Comput. Appl. Math. 97 1998 99-119
25. M.P. Brenner P. Constantin L.P. Kadanoff A. Schenkel S.C. Venkataramani Diffusion, attraction and collapse Nonlinearity 12 1999 1071-1098
26. L.R. Petzold A description of DASSL: A differential/algebrasystem system solver, SAND 82-8637 1982 Sandia Labs Livermore, CA
27. J. Dongarra J. Bunch C. Moler G.W. Stewart Linpack Users' Guide 1979 SIAM Philadelphia
28. E. Hairer G. Wanner Solving Ordinary Differential Equations II: Stiff and Differential Algebraic Problems Springer Series in Computational Mathematics 14 1996 Springer-Verlag Berlin
29. S. Childress J.K. Percus Nonlinear aspects of chemotaxis Math. Biosci. 56 1981 217-237
30. S. Childress Chemotactic collapse in two dimensions Lecture Notes in Biomathematics 55 1984 Springer-Verlag Berlin pp. 61-66
31. C.J. Budd, R. Carretero-González, R.D. Russell. Blow-up rings in chemotactic collapse, in preparation
32. G. Beckett J.A. Mackenzie On a uniform accurate finite difference approximation of a singularly perturbed reaction-diffusion problem using grid equidistribution J. Comput. Appl. Math. 131 (1-2) 2001 381-405