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- W2023763411 abstract "We consider boundary value problems for semilinear hyperbolic systems of the type∂tuj+aj(x,λ)∂xuj+bj(x,λ,u)=0,x∈(0,1),j=1,…,n, with smooth coefficient functions aj and bj such that bj(x,λ,0)=0 for all x∈[0,1], λ∈R, and j=1,…,n. We state conditions for Hopf bifurcation, i.e., for existence, local uniqueness (up to phase shifts), smoothness and smooth dependence on λ of time-periodic solutions bifurcating from the zero stationary solution. Furthermore, we derive a formula which determines the bifurcation direction. The proof is done by means of a Liapunov–Schmidt reduction procedure. For this purpose, Fredholm properties of the linearized system and implicit function theorem techniques are used." @default.
- W2023763411 created "2016-06-24" @default.
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- W2023763411 date "2014-07-01" @default.
- W2023763411 modified "2023-09-23" @default.
- W2023763411 title "Hopf bifurcation for semilinear dissipative hyperbolic systems" @default.
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- W2023763411 doi "https://doi.org/10.1016/j.jde.2014.04.003" @default.
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