The one-phase bifurcation for the p-Laplacian
Copyright policy )The one-phase bifurcation for the p-Laplacian
A bifurcation about the uniqueness of a solution of a singularly perturbed free boundary problem of phase transition associated with the p-Laplacian, subject to given boundary condition is proved in this paper. We show this phenomenon by proving the existence of a third solution through the Mountain Pass Lemma when the boundary data decreases below a threshold. In the second part, we prove the convergence of an evolution to stable solutions, and show the Mountain Pass solution is unstable in this sense.
19 pages
- Wayne State College United States
- Department of Mathematics
- Wayne State University United States
Bifurcations in context of PDEs, Mathematics - Analysis of PDEs, Quasilinear elliptic equations, bifurcation, FOS: Mathematics, Quasilinear elliptic equations with \(p\)-Laplacian, \(p\)-Laplacian, 35J92, 35J25, 35J62, 35K92, 35K20, 35K59, mountain pass theorem, Analysis of PDEs (math.AP)
Bifurcations in context of PDEs, Mathematics - Analysis of PDEs, Quasilinear elliptic equations, bifurcation, FOS: Mathematics, Quasilinear elliptic equations with \(p\)-Laplacian, \(p\)-Laplacian, 35J92, 35J25, 35J62, 35K92, 35K20, 35K59, mountain pass theorem, Analysis of PDEs (math.AP)
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