2026-06-08T14:53:56Zhttps://docta.ucm.es/rest/oai/requestoai:docta.ucm.es:20.500.14352/1247302025-10-09T23:48:06Zcom_20.500.14352_14col_20.500.14352_15
Docta Complutense
author
Arrieta Algarra, José María
author
Fernandes, Juliana
author
Lappicy, Phillipo
2025-10-09T11:34:32Z
2025-10-09T11:34:32Z
2025
Arrieta, J. M., Fernandes, J., & Lappicy, P. On bifurcation from infinity: a compactification approach. Calculus of Variations and Partial Differential Equations. 2025; 64(3): 1-18.
0944-26691432-0835
10.1007/s00526-025-02945-3
https://hdl.handle.net/20.500.14352/124730
We consider a scalar parabolic partial differential equation on the interval with nonlinear boundary conditions that are asymptotically sublinear. As the parameter crosses critical values (e.g. the Steklov eigenvalues), it is known that there are large equilibria that arise through a bifurcation from infinity (i.e., such equilibria converge, after rescaling, to the Steklov eigenfunctions). We provide a compactification approach to the study of such unbounded bifurcation curves of equilibria, their stability, and heteroclinic orbits. In particular, we construct an induced semiflow at infinity such that the Steklov eigenfunctions are equilibria. Moreover, we prove the existence of infinite-time blow-up solutions that converge, after rescaling, to certain eigenfunctions that are equilibria of the induced semiflow at infinity.
eng
Attribution 4.0 International
On bifurcation from infinity: a compactification approach
journal article
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3703407dfaa34558f54380c4e82c772e
711716
application/pdf
arrieta_bifurcation.pdf