• Publications
  • Influence
Initial value/boundary value problems for fractional diffusion-wave equations and applications to some inverse problems
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 ellipticExpand
  • 522
  • 53
  • PDF
Lipschitz stability in inverse parabolic problems by the Carleman estimate
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 aExpand
  • 171
  • 21
Carleman estimates for parabolic equations and applications
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 solutionsExpand
  • 191
  • 19
  • PDF
Uniqueness and stability in multidimensional hyperbolic inverse problems
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 theExpand
  • 152
  • 14
  • PDF
GLOBAL UNIQUENESS AND STABILITY IN DETERMINING COEFFICIENTS OF WAVE EQUATIONS
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 nExpand
  • 162
  • 13
Global Lipschitz stability in an inverse hyperbolic problem by interior observations
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, fromExpand
  • 167
  • 11
Determination of a coefficient in an acoustic equation with a single measurement
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 ofExpand
  • 108
  • 11
On a global estimate in a linear inverse hyperbolic problem
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 byExpand
  • 99
  • 10
The Calderón problem with partial data in two dimensions
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
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 weExpand
  • 142
  • 6