Stability of the Interface of a Hele–Shaw Flow with Two Injection Points
Resource
SIAM Journal on Mathematical Analysis, 43(4), 1810-1834
Journal
SIAM Journal on Mathematical Analysis
Journal Volume
43
Journal Issue
4
Pages
1810-1834
Date Issued
2011
Date
2011
Author(s)
Onodera, Michiaki
Abstract
We consider a Hele�VShaw 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.
Type
journal article
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