发表机构
Universidade Estadual de Campinas - UNICAMP; Instituto de Matemática, Estatística e Computação Científica - IMECC; Departamento de Matemática; Universidade Federal do Ceará（坎皮纳斯州立大学; 数学、统计与科学计算研究所; 数学系; 塞阿拉联邦大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究由g-拉普拉斯算子控制的单相自由边界问题，证明边界数据低于阈值时出现分岔，存在第三个解，并分析演化问题的渐近稳定性。
AI 中文摘要
在给定边界条件下，建立了由g-拉普拉斯算子控制的奇异摄动单相自由边界问题中的分岔现象。该分岔的特征在于，当边界数据降至适当阈值以下时，通过山路引理获得第三个解的存在性。此外，我们分析了相关演化问题的渐近行为，证明了其收敛到稳定的平稳解，并表明山路引理解在该动力学意义下是不稳定的。
英文摘要
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.
Comments22 pages. Comments are welcome
