Calcium waves in systems with immobile buffers as a limit of waves for systems with nonzero diffusion

Nonlinearity

Volumn 21, Issue 1, 2008, Pages 71-96

  Kaźmierczak, Bogdan ^a   Volpert, Vitaly ^b  

^a INSTITUTE OF FUNDAMENTAL TECHNOLOGICAL RESEARCH   (Poland)

^b UNIVERSITÉ LYON 1   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 38849146463     PISSN: 09517715     EISSN: 13616544     Source Type: Journal    
DOI: 10.1088/0951-7715/21/1/004     Document Type: Article

References (11)

1. Crandall M 1977 An introduction to constructive aspects of bifurcation theory and implicit function theorem Applications of Bifurcation Theory ed P Rabinowitz (New York: Academic)
2. Crooks E C M and Toland J F 1998 Travelling waves for reaction-diffusion-convection systems Topological Methods Nonlinear Anal. 11 19-43
3. 2+ signaling Adv. Phys. 53 255-440
4. Gantmacher F R 1960 The Theory of Matrices (New York: Chelsea)
5. Kazmierczak B and Volpert V 2003 Existence of heteroclinic orbits for systems satisfying monotonicity conditions Nonlinear Anal. 55 467-91
6. Palmer K J 1984 Exponential dichotomies and transversal homoclinic points J. Diff. Eqns 20 225-56
7. Shenq Guo J and Tsai J 2006 The asymptotic behavior of solutions of the buffered bistable system J. Math. Biol. 53 179-213
8. Sneyd J, Dale P D and Duffy A 1998 Traveling waves in buffered systems: applications to calcium waves SIAM J. Appl. Math. 58 1178-92
9. Taylor A E 1958 Introduction to Functional Analysis (New York: Wiley)
10. Tsai J and Sneyd J 2005 Existence and stability of traveling waves in buffered systems SIAM J. Appl. Math. 66 237-65
11. Volpert A, Volpert V and Volpert V 1994 Travelling Wave Solutions of Parabolic Systems (Providence, RI: American Mathematical Society)