Abstract
AbstractIn this paper we study the following parabolic system $$\begin{aligned} \Delta \mathbf{u }-\partial _t \mathbf{u }=|\mathbf{u }|^{q-1}\mathbf{u }\,\chi _{\{ |\mathbf{u }|>0 \}}, \qquad \mathbf{u }= (u^1, \cdots , u^m) \ , \end{aligned}$$
Δ
u
-
∂
t
u
=
|
u
|
q
-
1
u
χ
{
|
u
|
>
0
}
,
u
=
(
u
1
,
⋯
,
u
m
)
,
with free boundary $$\partial \{|\mathbf{u }| >0\}$$
∂
{
|
u
|
>
0
}
. For $$0\le q<1$$
0
≤
q
<
1
, we prove optimal growth rate for solutions $$\mathbf{u }$$
u
to the above system near free boundary points, and show that in a uniform neighbourhood of any a priori well-behaved free boundary point the free boundary is $$C^{1, \alpha }$$
C
1
,
α
in space directions and half-Lipschitz in the time direction.
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Analysis
Cited by
2 articles.
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