Nonexistence of monotonic solutions of some third-order ode relevant to the Kuramoto-Sivashinsky equation

Taiwanese Journal of Mathematics

Volumn 4, Issue 4, 2000, Pages 621-625

  Ishimura, Naoyuki ^a   Nakamura, MasaAki ^b  

^a HITOTSUBASHI UNIVERSITY   (Japan)

^b NIHON UNIVERSITY   (Japan)

Author keywords

Kuramoto Sivashinsky equation; Monotonic solution

Indexed keywords

EID: 0000750860     PISSN: 10275487     EISSN: None     Source Type: Journal    
DOI: 10.11650/twjm/1500407295     Document Type: Article

References (17)

1. C. Amick and J. B. McLeod, A singular perturbation problem in needle crystals, Arch. Rational Mech. Anal. 109 (1990), 139-171.
2. F. Bernis, L. A. Peletier and S. M. Williams, Source type solutions of a fourth order nonlinear degenerate parabolic equation, Nonlinear Anal. 18 (1992), 217-234.
3. M. Gregus, Third Order Linear Differential Equations, D. Reidel Publishing Company, Dordrecht, 1987.
4. R. Grimshaw and A. P. Hooper, The non-existence of a certain class of travelling wave solutions of the Kuramoto-Sivashinsky equation, Phys. D 50 (1991), 231-238.
5. J. M. Hammersley and G. Mazzarino, A differential equation connected with the dendritic growth of crystals, IMA J. Appl. Math. 42 (1989), 43-75.
6. N. Ishimura and M. A. Nakamura, A note on the nonexistence of monotonic steady solutions of the Kuramoto-Sivashinsky equation, preprint.
7. J. Jones, W. C. Troy and A. D. MacGillivary, Steady solutions of the Kuramoto-Sivashinsky equation for small wave speed, J. Differential Equations 96 (1992), 28-55.
8. M. D. Kruskal and H. Segur, Asymptotics beyond all orders in a model of crystal growth, Stud. Appl. Math. 85 (1991), 129-181.
9. Y. Kuramoto and T. Tsuzuki, Persistent propagation of concentration waves in dissipative media far from thermal equilibrium, Progr. Theoret. Phys. 55 (1976), 356-369.
10. Y. Kuramoto and T. Yamada, Turbulent state in chemical reaction, Progr. Theoret. Phys. 56 (1976), 679.
11. J. S. Langer, Existence of needle crystals in local models of solidification, Phys. Rev. A 33 (1986), 435-441.
12. D. Michelson, Steady solutions of the Kuramoto-Sivashinsky equation, Phys. D 19 (1986), 89-111.
13. D. M. Michelson and G. I. Sivashinsky, Nonlinear analysis of hydrodynamic instability in laminar flames II. Numerical experiments, Acta Astronautica 4 (1977), 1207-1221.
14. G. I. Sivashinsky, Nonlinear analysis of hydrodynamic instability in laminar flames I. Derivation of basic equations, Acta Astronautica 4 (1977), 1177-1206.
15. J. F. Toland, Existence and uniqueness of heteroclinic orbits for the equation λu‴ + u′ = f(u), Proc. Roy. Soc. Edinburgh Sect. A 109 (1988), 23-36.
16. W. C. Troy, The existence of steady solutions of the Kuramoto-Sivashinsky equation, J. Differential Equations 82 (1989), 269-313.
17. W. C. Troy, Nonexistence of monotonic solutions in a model of dendritic growth, Quart. Appl. Math. 48 (1990), 209-215.