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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
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
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
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
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
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
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
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
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
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