On travelling waves in a suspension bridge model as the wave speed goes to zero
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.
scientific article; zbMATH DE number 5907674
scientific article