Details
| Originalsprache | Englisch |
|---|---|
| Seiten (von - bis) | 1441-1471 |
| Seitenumfang | 31 |
| Fachzeitschrift | Communications in Partial Differential Equations |
| Jahrgang | 41 |
| Ausgabenummer | 9 |
| Publikationsstatus | Veröffentlicht - 10 Sept. 2016 |
Abstract
We consider the porous medium equation on manifolds with conical singularities and show existence, uniqueness, and maximal Lp-regularity of a short-time solution. In particular, we obtain information on the short time asymptotics of the solution near the conical point. Our method is based on bounded imaginary powers results for cone differential operators on Mellin–Sobolev spaces and R-sectoriality perturbation techniques.
ASJC Scopus Sachgebiete
- Mathematik (insg.)
- Analysis
- Mathematik (insg.)
- Angewandte Mathematik
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in: Communications in Partial Differential Equations, Jahrgang 41, Nr. 9, 10.09.2016, S. 1441-1471.
Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review
}
TY - JOUR
T1 - Existence and maximal Lp-regularity of solutions for the porous medium equation on manifolds with conical singularities
AU - Roidos, Nikolaos
AU - Schrohe, Elmar
N1 - Publisher Copyright: © 2016, Copyright © Taylor & Francis Group, LLC. Copyright: Copyright 2016 Elsevier B.V., All rights reserved.
PY - 2016/9/10
Y1 - 2016/9/10
N2 - We consider the porous medium equation on manifolds with conical singularities and show existence, uniqueness, and maximal Lp-regularity of a short-time solution. In particular, we obtain information on the short time asymptotics of the solution near the conical point. Our method is based on bounded imaginary powers results for cone differential operators on Mellin–Sobolev spaces and R-sectoriality perturbation techniques.
AB - We consider the porous medium equation on manifolds with conical singularities and show existence, uniqueness, and maximal Lp-regularity of a short-time solution. In particular, we obtain information on the short time asymptotics of the solution near the conical point. Our method is based on bounded imaginary powers results for cone differential operators on Mellin–Sobolev spaces and R-sectoriality perturbation techniques.
KW - Conically degenerate operators
KW - fast diffusion equation
KW - Fuchs type operators
KW - manifolds with conical singularities
KW - maximal L-regularity
KW - porous medium equation
UR - http://www.scopus.com/inward/record.url?scp=84986201474&partnerID=8YFLogxK
U2 - 10.1080/03605302.2016.1219745
DO - 10.1080/03605302.2016.1219745
M3 - Article
AN - SCOPUS:84986201474
VL - 41
SP - 1441
EP - 1471
JO - Communications in Partial Differential Equations
JF - Communications in Partial Differential Equations
SN - 0360-5302
IS - 9
ER -