Year: 2026
Type: preprint
Abstract: The bifurcation phenomenon in a singularly perturbed one-phase free boundary problem governed by the g-Laplacian is established under prescribed boundary conditions. This bifurcation is characterized by the existence of a third solution, obtained via the Mountain Pass Lemma, when the boundary data decreases below a suitable threshold. Moreover, we analyze the asymptotic behavior of the associated evolution problem, proving convergence to stable stationary solutions and showing that the Mountain Pass solution is unstable in this dynamical sense.
Source: arXiv (Cornell University)
Authors: Bessa, Junior da Silva, Sousa, Alan Pio
Institution: Universidade Federal do Ceará
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Award: G4934132679
OpenAlex ID: W7214508259