MR3012578
Katsuju IGARI
Katsuju IGARI
Stationary Strings in Air Flows and a Non-Linear Boundary Value Problem
Funkcialaj Ekvacioj. Serio Internacia
55
2012
285--300
http://fe.math.kobe-u.ac.jp/FE/FullPapers/55-2/55_285.pdf
http://www.ams.org/mathscinet-getitem?mr=MR3012578
We consider stationary states of a string with one end fixed in air flows. Describing with a boundary value problem, we study how many stationary states there exist and if they are locally unique and stable. A bifurcation phenomenon of stationary states will be found.
Stationary strings in air flows, Non-linear boundary value problem, Bifurcation.
34B15, 34C23, 74K05.
55-285
2012
Stationary Strings in Air Flows and a Non-Linear Boundary Value Problem
Katsuju IGARI
Katsuju IGARI
1
Kaneko, A.
Introduction to partial differential equations
(in Japanese), Univ. Tokyo Press
1998
2
Koshlyakov, N. S.; Gliner, E. B.; Smirnov, M. M.
Differential equations of mathematical physics
Gosudarstv. Izdat. Fiz.-Mat. Lit., Moscow
1962
MR0158145
3
Morikawa, K.; Ayukawa, K.; Tsuji, Y.
Fluid Dynamics
("Nagaregaku", in Japanese), Asakura Publishing Co., Ltd.
1993
4
Petrovski, I. G.
Ordinary differential equations
Dover
1973
MR0193298
5
Preston, S. C.
The motion of whips and chains
J. Differential Equations
251
2011
504-550
MR2802023
6
Reeken, M.
Classical solutions of the chain equation. I
Math. Z.
165
1979
143-169
MR0520818
7
Yamaguchi, M.
Almost periodic oscillations of suspended string under quasiperiodic linear force
J. Math. Anal. Appl.
303
2005
643-660
MR2122567