Abstract
Abstract
We prove existence and uniqueness of the branch of the so-called anomalous eternal solutions in exponential self-similar form for the subcritical fast-diffusion equation with a weighted reaction term
∂
t
u
=
Δ
u
m
+
|
x
|
σ
u
p
,
posed in
R
N
with N ⩾ 3, where
1,$?>
0
<
m
<
m
c
=
N
−
2
N
,
p
>
1
,
and the critical value for the weight
σ
=
2
(
p
−
1
)
1
−
m
.
The branch of exponential self-similar solutions behaves similarly as the well-established anomalous solutions to the pure fast diffusion equation, but without a finite time extinction or a finite time blow-up, and presenting instead a change of sign of both self-similar exponents at m = m
s = (N − 2)/(N + 2), leading to surprising qualitative differences. In this sense, the reaction term we consider realizes a perfect equilibrium in the competition between the fast diffusion and the reaction effects.
Subject
Applied Mathematics,General Physics and Astronomy,Mathematical Physics,Statistical and Nonlinear Physics
Cited by
3 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献