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Article Contents

# Self-excited vibrations for damped and delayed higher dimensional wave equations

• * Corresponding author: Nemanja Kosovalić
• In the article [12] it is shown that time delay induces self-excited vibrations in a one dimensional damped wave equation. Here we generalize this result for higher spatial dimensions. We prove the existence of branches of nontrivial time periodic solutions for spatial dimensions $d\ge 2$. For $d> 2$, the bifurcating periodic solutions have a fixed spatial frequency vector, which is the solution of a certain Diophantine equation. The case $d = 2$ must be treated separately from the others. In particular, it is shown that an arbitrary number of symmetry breaking orbitally distinct time periodic solutions exist, provided $d$ is big enough, with respect to the symmetric group action. The direction of bifurcation is also obtained.

Mathematics Subject Classification: Primary: 35L05; Secondary: 37K50.

 Citation:

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