Please use this identifier to cite or link to this item: http://hdl.handle.net/10077/30768
Title: Global structure of bifurcation curves related to inverse bifurcation problems
Authors: Shibata, Tetsutaro
Keywords: precise structure of bifurcation curvesoscillatory nonlinear diffusioninverse bifurcation problems
Issue Date: 2020
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
Journal: Rendiconti dell’Istituto di matematica dell’Università di Trieste: an International Journal of Mathematics 
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).
Type: Article
URI: http://hdl.handle.net/10077/30768
ISSN: 0049-4704
eISSN: 2464-8728
DOI: 10.13137/2464-8728/30768
Rights: Attribution-NonCommercial-NoDerivatives 4.0 Internazionale
Appears in Collections:Rendiconti dell’Istituto di Matematica dell’Università di Trieste: an International Journal of Mathematics vol.52 (2020), in progress

Files in This Item:
File Description SizeFormat
A3_Shibata.pdf322.23 kBAdobe PDFThumbnail
View/Open
Show full item record


CORE Recommender

Page view(s)

59
checked on Oct 25, 2020

Download(s)

4
checked on Oct 25, 2020

Google ScholarTM

Check

Altmetric

Altmetric


This item is licensed under a Creative Commons License Creative Commons