The saddle point property for focusing selfsimilar solutions in a free boundary problem

Brauner, Claude‐Michel; Hulshof, Josephus; Schmidt-Lainé, Claudine

doi:10.1090/s0002-9939-99-04829-7

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Cited by 3 publications

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“…). To linearize the system around this equilibrium, we follow the method developed in [4,5,6]. For this purpose, first of all we introduce the function Ỹ , Θ, Ũ defined by Ỹ (x) = Y (Rx), Θ(x) = Θ(Rx), Ũ (x) = RU (Rx).…”

Section: Function Spacesmentioning

confidence: 99%

Instability in a flame ball problem

Guyonne¹,

Lorenzi²

2007

Discrete &Amp; Continuous Dynamical Systems - B

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Section: Function Spacesmentioning

confidence: 99%

Instability in a flame ball problem

Guyonne¹,

Lorenzi²

2007

Discrete &Amp; Continuous Dynamical Systems - B

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A General Approach to Stability in Free Boundary Problems

Brauner

Hulshof²,

Lunardi

2000

Journal of Differential Equations

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Every solution of a linear elliptic equation on a bounded domain may be considered as an equilibrium of a free boundary problem. The free boundary problem consists of the corresponding parabolic equation on a variable unknown domain with free boundary conditions prescribing both Dirichlet and Neumann data. We establish a rigorous stability analysis of such equilibria, including the construction of stable and unstable manifolds. For this purpose we transform the free boundary problem to a fully nonlinear and nonlocal parabolic problem on a fixed domain with fully nonlinear lateral boundary conditions and we develop the general theory for such problems. As an illustration we give two examples, the second being the focussing flame problem in combustion theory. Academic Press

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