Affiliation:
1. CAS Wu Wen-Tsun Key Laboratory of Mathematics , School of Mathematical Sciences , University of Science and Technology of China , 96 Jinzhai Road Baohe , Hefei , Anhui, 230026 , P. R. China
2. Mathematics & Science College , Shanghai Normal University , 100 Guilin Road , Shanghai , 200234 , P. R. China
Abstract
Abstract
In this paper, we consider Carleman estimates and inverse problems for the coupled quantitative thermoacoustic equations. In part I, we establish Carleman estimates for the coupled quantitative thermoacoustic equations
by assuming that the coefficients satisfy suitable conditions and taking the usual weight function
φ
(
x
,
t
)
=
e
λ
ψ
(
x
,
t
)
,
ψ
(
x
,
t
)
=
|
x
-
x
0
|
2
-
β
|
t
-
t
0
|
2
+
β
t
0
2
\varphi(x,t)={\mathrm{e}}^{\lambda\psi(x,t)},\quad\psi(x,t)=\lvert x-x_{0}%
\rvert^{2}-\beta\lvert t-t_{0}\rvert^{2}+\beta t_{0}^{2}
for x in a bounded domain in
ℝ
n
{\mathbb{R}^{n}}
with
C
3
{C^{3}}
-boundary
and
t
∈
(
0
,
T
)
{t\in(0,T)}
, where
t
0
=
T
2
{t_{0}=\frac{T}{2}}
.
We will discuss applications of the Carleman estimates to some inverse problems for the coupled quantitative thermoacoustic equations in
the succeeding part II paper
[M. Cristofol, S. Li and Y. Shang,
Carleman estimates and inverse problems for the coupled quantitative thermoacoustic equations. Part II: Inverse problems,
preprint 2020, https://hal.archives-ouvertes.fr/hal-02863385].
Cited by
2 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献