Global existence and uniqueness for the inhomogeneous 1-Laplace evolution equation
In this paper we introduce a new approach to the Dirichlet problem for the total variation flow in a bounded domain and analyze the associated inhomogeneous problem. We prove global existence and uniqueness for source data belonging to L l o c 1 ( 0 , + ∞ ; L 2 ( Ω ) ) and L 2 -initial data. We comp...
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| Veröffentlicht in: | Nonlinear differential equations and applications 2015-10, Vol.22 (5), p.1213-1246 |
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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | In this paper we introduce a new approach to the Dirichlet problem for the total variation flow in a bounded domain and analyze the associated inhomogeneous problem. We prove global existence and uniqueness for source data belonging to
L
l
o
c
1
(
0
,
+
∞
;
L
2
(
Ω
)
)
and
L
2
-initial data. We compare solutions corresponding to different data as well as study the long-term behaviour of the solutions. We also show explicit examples of radial solutions. |
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| ISSN: | 1021-9722 1420-9004 |
| DOI: | 10.1007/s00030-015-0320-7 |