CORE
πΊπ¦Β
Β make metadata, not war
Services
Services overview
Explore all CORE services
Access to raw data
API
Dataset
FastSync
Content discovery
Recommender
Discovery
OAI identifiers
OAI Resolver
Managing content
Dashboard
Bespoke contracts
Consultancy services
Support us
Support us
Membership
Sponsorship
Community governance
Advisory Board
Board of supporters
Research network
About
About us
Our mission
Team
Blog
FAQs
Contact us
Well-posedness for a molecular beam epitaxy model
Authors
Daniel Oliveira da Silva
Louis Emerald
Achenef Tesfahun
Publication date
28 November 2023
Publisher
View
on
arXiv
Abstract
We study a general molecular beam epitaxy (MBE) equation modeling the epitaxial growth of thin films. We show that, in the deterministic case, the associated Cauchy problem admits a unique smooth solution for all time, given initial data in the space
X
0
=
L
2
(
R
d
)
β©
W
Λ
1
,
4
(
R
d
)
X_0 = L^{2}(R^{d}) \cap \dot{W}^{1,4}(R^{d})
X
0
β
=
L
2
(
R
d
)
β©
W
Λ
1
,
4
(
R
d
)
with
d
=
1
,
2
d = 1, 2
d
=
1
,
2
. This improves a recent result by Ag\'elas, who established global existence in
H
3
(
R
d
)
H^{3}(R^{d})
H
3
(
R
d
)
. Moreover, we investigate the local existence and uniqueness of solutions in the space
X
0
X_0
X
0
β
for the stochastic MBE equation, with an additive noise that is white in time and regular in the space variable
Similar works
Full text
Available Versions
arXiv.org e-Print Archive
See this paper in CORE
Go to the repository landing page
Download from data provider
oai:arXiv.org:2311.16970
Last time updated on 10/05/2024