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  4. Rendiconti dell’Istituto di Matematica dell’Università di Trieste: an International Journal of Mathematics
  5. Rendiconti dell’Istituto di Matematica dell’Università di Trieste: an International Journal of Mathematics vol.52 (2020), 1st and 2nd Issue
  6. Global structure of bifurcation curves related to inverse bifurcation problems
 
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Global structure of bifurcation curves related to inverse bifurcation problems

Shibata, Tetsutaro
2020
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ISSN
0049-4704
DOI
10.13137/2464-8728/30768
http://hdl.handle.net/10077/30768
  • Article

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).
Journal
Rendiconti dell’Istituto di matematica dell’Università di Trieste: an International Journal of Mathematics 
Subjects
  • precise structure of ...

  • oscillatory nonlinear...

  • inverse bifurcation p...

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
Licence
http://creativecommons.org/licenses/by-nc-nd/4.0/
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