On travelling waves in a suspension bridge model as the wave speed goes to zero. (English) Zbl 1228.34065
The authors are concerned with finding homoclinic solutions to the equation
\[
y'''+ c^2 y''+ (1+ y)^+- 1= 0,\tag{\(*\)}
\]
which are related to travelling wave solutions with speed \(c\) to \(u_{tt}+ u_{xxxx}+ u^+= 1\). They prove that as \(c\to 0\), all solutions of \((*)\) tend to \(+\infty\) in the \(L^\infty\)-norm.
Reviewer: Klaus R. Schneider (Berlin)
MSC:
| 34C37 | Homoclinic and heteroclinic solutions to ordinary differential equations |
| 34B40 | Boundary value problems on infinite intervals for ordinary differential equations |
| 34C11 | Growth and boundedness of solutions to ordinary differential equations |
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