A Priori Estimates for Fractional Nonlinear Degenerate Diffusion Equations on Bounded Domains
We investigate quantitative properties of the nonnegative solutions u ( t , x ) ≥ 0 to the nonlinear fractional diffusion equation, ∂ t u + L ( u m ) = 0 , posed in a bounded domain, x ∈ Ω ⊂ R N , with m > 1 for t > 0. As L we use one of the most common definitions of the fractional Laplacia...
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| Veröffentlicht in: | Archive for rational mechanics and analysis 2015-10, Vol.218 (1), p.317-362 |
|---|---|
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | We investigate quantitative properties of the nonnegative solutions
u
(
t
,
x
)
≥
0
to the nonlinear fractional diffusion equation,
∂
t
u
+
L
(
u
m
)
=
0
, posed in a bounded domain,
x
∈
Ω
⊂
R
N
, with
m
> 1 for
t
> 0. As
L
we use one of the most common definitions of the fractional Laplacian
(
-
Δ
)
s
, 0 |
|---|---|
| ISSN: | 0003-9527 1432-0673 |
| DOI: | 10.1007/s00205-015-0861-2 |