Existence of Self-Similar Solutions to a Parabolic System Modelling Chemotaxis

Japan Journal of Industrial and Applied Mathematics

Volumn 17, Issue 3, 2000, Pages 427-451

  Muramoto, Naomi ^a   Naito, Yuki ^b   Yoshida, Kiyoshi ^a  

^a HIROSHIMA UNIVERSITY   (Japan)

^b KOBE UNIVERSITY   (Japan)

Author keywords

Chemotaxis; Elliptic equation; Global branch; Self similar solution

Indexed keywords

EID: 0010784598     PISSN: 09167005     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF03167376     Document Type: Article

References (15)

1. P. Biler, Local and global solvability of some parabolic systems modelling chemotaxis. Adv. Math. Sci. Appl., 8 (1998), 715-743.
2. S. Childress, Chemotactic collapse in two dimensions. Lecture Notes in Biomath., 55, Springer, 1984, 217-237.
3. S. Childress and J.K. Percus, Nonlinear aspects of chemotaxis. Math. Biosci., 56(1981), 217-237.
4. R. Courant and D. Hilbert, Method of Mathematical Physics, Vol. 1. Interscience, 1953.
5. M.G. Crandall and P.H. Rabinowitz, Some continuation and variational methods for positive solutions of nonlinear elliptic eigenvalue problems. Arch. Rational Mech. Anal., 58 (1975), 207-218.
6. M. Escobedo and O. Kavian, Variational problems related to self-similar solutions of the heat equation. Nonlinear Anal., 11 (1987), 1103-1133.
7. D. Gillbarg and N. Trudinger, Elliptic Partial Differential Eqautions of Second Order (2nd ed.). Springer, 1983.
8. S. Kawashima, Self-similar solutions of a convection-diffusion equation. Lecture Notes in Numer. Appl. Anal., 12 (1993), 123-136.
9. E.F. Keller and L.A. Segel, Initiation of slime mold aggregation viewed as an instability. J. Theor. Biol., 26 (1970), 399-415.
10. Y. Mizutani and T. Nagai, Self-similar radial solutions to a system of partial differential equations modelling chemotaxis. Bull. Kyushu Inst. Tech. (Math. Natur. Sci.), 42 (1995), 19-28.
11. Y. Mizutani, N. Muramoto and K. Yoshida, Self-similar radial solutions to a parabolic system modelling chemotaxis via variational method. Hiroshima Math. J., 29 (1999), 145-160.
12. T. Nagai, T. Senba and K. Yoshida, Application of the Trudinger-Moser inequality to a parabolic system of chemotaxis. Funkcialaj Ekvacioj, 40 (1997), 411-433.
13. T. Ogawa, A proof of Trudinger's inequality and its application to nonlinear Schrödinger equations. Nonlinear Anal., 14 (1990), 765-769.
14. D.H. Sattinger, Monotone methods in nonlinear elliptic and parabolic boundary value problems. Indiana Univ. Math. J., 21 (1972), 979-1000.
15. T. Suzuki, Semilinear Elliptic Equations. Gakkōtosho, 1994.