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State-constraint static Hamilton-Jacobi equations in nested domains
Authors
Yeoneung Kim
Hung V. Tran
Son N. T. Tu
Publication date
26 June 2019
Publisher
View
on
arXiv
Abstract
We study state-constraint static Hamilton-Jacobi equations in a sequence of domains
{
Ξ©
k
}
k
β
N
\{\Omega_k\}_{k \in \mathbb{N}}
{
Ξ©
k
β
}
k
β
N
β
in
R
n
\mathbb{R}^n
R
n
such that
Ξ©
k
β
Ξ©
k
+
1
\Omega_k \subset \Omega_{k+1}
Ξ©
k
β
β
Ξ©
k
+
1
β
for all
k
β
N
k\in \mathbb{N}
k
β
N
. We obtain rates of convergence of
u
k
u_k
u
k
β
, the solution to the state-constraint problem in
Ξ©
k
\Omega_k
Ξ©
k
β
, to
u
u
u
, the solution to the corresponding problem in
Ξ©
=
β
k
β
N
Ξ©
k
\Omega = \bigcup_{k \in \mathbb{N}} \Omega_k
Ξ©
=
β
k
β
N
β
Ξ©
k
β
. In many cases, the rates obtained are proven to be optimal. Various new examples and discussions are provided at the end of the paper.Comment: 23 pages, 1 figur
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oai:arXiv.org:1906.11222
Last time updated on 12/10/2020