Stability of the Interface of a Hele–Shaw Flow with Two Injection Points | Zendy

Michiaki Onodera | Zendy

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Stability of the Interface of a Hele–Shaw Flow with Two Injection Points

Author(s) -

Michiaki Onodera

Publication year - 2011

Publication title -

siam journal on mathematical analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.882

H-Index - 92

eISSN - 1095-7154

pISSN - 0036-1410

DOI - 10.1137/110821603

Subject(s) - mathematics , hele shaw flow , domain (mathematical analysis) , boundary (topology) , flow (mathematics) , infinity , stability (learning theory) , free boundary problem , algebraic number , interface (matter) , boundary value problem , mathematical analysis , algebraic equation , geometry , mechanics , nonlinear system , open channel flow , physics , computer science , bubble , machine learning , maximum bubble pressure method , quantum mechanics

We consider a Hele–Shaw flow produced by the injection of fluid at two points. A free boundary problem for the flow is formulated to describe the evolution of the interface between the fluid and the air. We present an explicit formula for the interface starting from a certain initial domain. Our aim is to study the stability of the interface under disturbance. We convert the free boundary problem to an evolution equation on a fixed domain. By means of the theory of analytic semigroups, we prove that the disturbance decays with algebraic order as time goes to infinity.

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