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Global structure of bifurcation curves related to inverse bifurcation problems
Shibata, Tetsutaro
2020
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e-ISSN
2464-8728
Abstract
We consider the nonlinear eigenvalue problem
[D(u(t))u(t)']' + λg(u(t)) = 0,
u(t) > 0 ; t ∈ I := (0, 1), u(0) = u(1) = 0,
which comes from the porous media type equation. Here, D(u) = pu2n+sin u (n ∈ N, p > 0: given constants), g(u) = u or g(u) = u + sin u. λ > 0 is a bifurcation parameter which is a continuous function of α = ||uλ||∞ of the solution uλ corresponding to λ, and is expressed as λ = λ(α). Since our equation contains oscillatory term in diffusion term, it seems significant to study how this oscillatory term gives effect to the structure of bifurcation curves λ(α). We propose a question from a view point of inverse bifurcation problems and show that the simplest case D(u) = u2 + sin u and g(u) = u gives us the most impressible asymptotic formula for global behavior of λ(α).
Publisher
EUT Edizioni Università di Trieste
Source
Tetsutaro Shibata, "Global structure of bifurcation curves related to inverse bifurcation problems" in: "Rendiconti dell’Istituto di matematica dell’Università di Trieste: an International Journal of Mathematics vol. 52 (2020)", EUT Edizioni Università di Trieste, Trieste, 2020
Languages
en
Rights
Attribution-NonCommercial-NoDerivatives 4.0 Internazionale
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