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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Inverse problem for the harmonic measure
谐波测量 反问题 双曲群
2023/4/13
Sample paths of a random walk on a hyperbolic group are known to converge to the Gromov boundary. The distribution of the exit point is called the harmonic measure. I will discuss the following invers...
An Inverse Problem for Gibbs Fields with Hard Core Potential
Gibbs Field Gibbs Measure Cluster Functions Pair Potential Corre-lation Functions Ursell Functions
2015/9/28
It is well known that for a regular stable potential of pair interaction and a small value of activity one can define the corresponding Gibbs field (a measure on the space of configurations of points ...
Solution of the Inverse Problem of Linear Optimal Control with Positiveness Conditions and Relation to Sensitivity
Linear Optimal Control Positiveness Conditions
2015/6/23
The property that the feedback control minimizes some performance index (1.3)
with Q ≥ 0 is of considerable interest because of its connection with the ability
of the control to reduce the sensitivi...
A parabolic inverse problem with mixed boundary data. Stability estimates for the unknown boundary and impedance
parabolic inverse problem unknown boundary and impedance Analysis of PDEs
2011/7/26
Abstract: We consider the problem of determining an unaccessible part of the boundary of a conductor by mean of thermal measurements. We study a problem of corrosion where a Robin type condition is pr...
Global uniqueness and reconstruction for the multi-channel Gel'fand-Calderón inverse problem in two dimensions
Global uniqueness reconstruction multi-channel Gel'fand-Calderón inverse problem
2010/12/31
We study the multi-channel Gel’fand-Calderón inverse problem in two dimensions, i.e. the inverse boundary value problem for the equation − + v(x) = 0, x 2 D, where v is a smooth matrix-valued...
An inverse problem of Calderon type with partial data
inverse problem of Calderon type partial data
2010/12/31
A generalized variant of the Calder´on problem from electrical impedance tomography with partial data for anisotropic Lipschitz conductivities is considered in an arbitrary space dimension n 2...
Exponential instability in the Gel'fand inverse problem on the energy intervals
Exponential instability Gel'fand inverse problem energy intervals
2010/12/31
We consider the Gel’fand inverse problem and continue studies of [Mandache,2001].We show that the Mandache-type instability remains valid even in the case of Dirichletto-Neumann map given on the energ...
Uniqueness for a hyperbolic inverse problem with angular control on the coefficients
Inverse Problems Wave Equation
2010/12/31
Suppose qi(x), i = 1; 2 are smooth functions on R3 and Ui(x; t) the solutions of the initial
value problem @2 t Ui Ui qi(x)Ui = (x; t); (x; t) 2 R3 R Ui(x; t) = 0; for t < 0...
On an inverse problem for a class of Dirac operator with discontinuous coefficient and a spectral parameter in the boundary condition
Dirac operator scattering function main equation
2010/12/30
In this paper, it is examined on the half line the inverse problem of scattering theory for a class Dirac operator with discontinuous coefficient and a spectral parameter in the boundary condition . T...
An inverse problem for the wave equation with one measurement and the pseudorandom noise
the wave equation measurement the pseudorandom noise
2010/11/1
We consider the wave equation $(\p_t^2-\Delta_g)u(t,x)=f(t,x)$, in $\R^n$, $u|_{\R_-\times \R^n}=0$, where the metric $g=(g_{jk}(x))_{j,k=1}^n$ is known outside an open and bounded set $M\subset \R^n...
Determination of time-dependent coefficients for a hyperbolic inverse problem
time-dependent coefficients hyperbolic inverse problem
2010/9/22
We consider an inverse boundary value problem for the hyperbolic partial differential equation
(−i@t+A0(t, x))2u(t, x)−Xn j=1−i@xj+Aj(t, x)2 u(t, x)+V (t, x)u(t, x) = 0 w...
A QUASI-NEWTON METHOD IN INFINITE-DIMENSIONAL SPACES AND ITS APPLICATIONFOR SOLVING A PARABOLIC INVERSE PROBLEM
Quasi-Newton method parabolic differential equation inverse problems in partial differential equations linear and Q-superlinear rates of convergence
2007/12/12
A Quasi-Newton method in Infinite-dimensional Spaces (QNIS) for solving
operator equations is presented and the convergence of a sequence
generated by QNIS is also proved in the paper. Next, we sugg...
The inverse problem of finding the refraction coefficient of a shallow ocean from the observation of the extra Cauchy data for the acoustic field at the surface of the ocean is studied. Uniqueness the...