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Publications Influence

Initial value/boundary value problems for fractional diffusion-wave equations and applications to some inverse problems

- K. Sakamoto, Masahiro Yamamoto
- Mathematics
- 1 October 2011

Abstract We consider initial value/boundary value problems for fractional diffusion-wave equation: ∂ t α u ( x , t ) = L u ( x , t ) , where 0 α ⩽ 2 , where L is a symmetric uniformly elliptic… Expand

522 53- PDF

Lipschitz stability in inverse parabolic problems by the Carleman estimate

- O. Imanuvilov, Masahiro Yamamoto
- Mathematics
- 1 October 1998

We consider a system with a suitable boundary condition, where is a bounded domain, is a uniformly elliptic operator of the second order whose coefficients are suitably regular for , is fixed, and a… Expand

171 21

Carleman estimates for parabolic equations and applications

- Masahiro Yamamoto
- Mathematics
- 1 December 2009

In this review, concerning parabolic equations, we give self-contained descriptions on derivations of Carleman estimates; methods for applications of the Carleman estimates to estimates of solutions… Expand

191 19- PDF

Uniqueness and stability in multidimensional hyperbolic inverse problems

- Masahiro Yamamoto
- Mathematics
- 1999

Abstract Under a weak regularity assumption, we prove the uniqueness in multidimensional hyperbolic inverse problems with a single measurement. Moreover we show that our uniqueness results yield the… Expand

152 14- PDF

GLOBAL UNIQUENESS AND STABILITY IN DETERMINING COEFFICIENTS OF WAVE EQUATIONS

- O. Imanuvilov, Masahiro Yamamoto
- Mathematics
- 30 June 2001

We consider an inverse problem of determining p(x), x ∈ Ω in (∂2 u/∂t 2)(x, t) − Δu(x, t) − p(x)u(x, t) = 0 in Ω × (0, T) and (∂u/∂ν)|∂Ω×(0, T) = 0 with given u(·, 0) and (∂u/∂t)(·, 0). Here Ω ⊂ R n… Expand

162 13

Global Lipschitz stability in an inverse hyperbolic problem by interior observations

- O. Imanuvilov, Masahiro Yamamoto
- Mathematics
- 1 August 2001

For the solution u(p) = u(p)(x,t) to ∂t2u(x,t)-Δu(x,t)-p(x)u(x,t) = 0 in Ω×(0,T) and (∂u/∂ν)|∂Ω×(0,T) = 0 with given u(,0) and ∂tu(,0), we consider an inverse problem of determining p(x), xΩ, from… Expand

167 11

Determination of a coefficient in an acoustic equation with a single measurement

- O. Imanuvilov, Masahiro Yamamoto
- Mathematics
- 1 February 2003

For the solution u(p) = u(p)(t, x) to ∂t2 u(t, x) − div(p(x)∇u(t, x)) = 0 in (0, T) × Ω with given u|(0,T)×∂Ω, u(0, ·) and ∂t u(0, ·), we consider an inverse problem concerning the determination of… Expand

108 11

On a global estimate in a linear inverse hyperbolic problem

- J. Puel, Masahiro Yamamoto
- Mathematics
- 1 December 1996

We show a global Lipschitz estimate in determining a source term in a hyperbolic equation from overdetermining data on the lateral boundary. The method is a combination of the uniqueness result by… Expand

99 10

The Calderón problem with partial data in two dimensions

- O. Imanuvilov, G. Uhlmann, Masahiro Yamamoto
- Mathematics
- 1 September 2010

We prove for a two dimensional bounded domain that the Cauchy data for the Schrodinger equation measured on an arbitrary open subset of the boundary determines uniquely the potential. This implies,… Expand

135 7- PDF

LETTER TO THE EDITOR: One new strategy for a priori choice of regularizing parameters in Tikhonov's regularization

- J. Cheng, Masahiro Yamamoto
- Mathematics
- 1 August 2000

In this paper, based on the conditional stability estimate for ill-posed inverse problems, we propose a new strategy for a priori choice of regularizing parameters in Tikhonov's regularization and we… Expand

142 6