Results 61 to 70 of about 4,144 (169)

Carleman Estimates for a Class of Degenerate Parabolic Operators [PDF]

SIAM Journal on Control and Optimization, 2008
Given $\alpha \in [0,2)$ and $f \in L^2 ((0,T)\times(0,1))$, we derive new Carleman estimates for the degenerate parabolic problem $w_t + (x^\alpha w_x) _x =f$, where $(t,x) \in (0,T) \times (0,1)$, associated to the boundary conditions $w(t,1)=0$ and $w(t,0)=0$ if $0 \leq \alpha
CANNARSA, PIERMARCO, MARTINEZ, P, VANCOSTENOBLE, J.   +2 more
openaire   +2 more sources

Global Lipschitz stability for an inverse coefficient problem for a mean field game system

Mathematical Methods in the Applied Sciences, Volume 48, Issue 3, Page 3858-3870, February 2025.
For an inverse coefficient problem of determining a state‐varying factor in the corresponding Hamiltonian for a mean field game system, we prove the global Lipschitz stability by spatial data of one component and interior data in an arbitrarily chosen subdomain over a time interval. The proof is based on Carleman estimates with different norms.
Oleg Imanuvilov, Masahiro Yamamoto
wiley   +1 more source

Inverse Source Problem for a Singular Parabolic Equation with Variable Coefficients

Mathematics
We consider a parabolic equation with a singular potential in a bounded domain Ω⊂Rn. The main result is a Lipschitz stability estimate for an inverse source problem of determining a spatial varying factor f(x) of the source term R(x,t)f(x).
Xue Qin, Shumin Li
doaj   +1 more source

Carleman estimates and inverse problems for Dirac operators [PDF]

Mathematische Annalen, 2008
20 pages; Proposition 2.4 concerning harmonic weights had an incorrect proof in the first version and has been removed, also other changes and ...
Salo, Mikko, Tzou, Leo
openaire   +2 more sources

The symplectic density property for Calogero–Moser spaces

Journal of the London Mathematical Society, Volume 111, Issue 2, February 2025.
Abstract We introduce the symplectic density property and the Hamiltonian density property together with the corresponding versions of Andersén–Lempert theory. We establish these properties for the Calogero–Moser space Cn$\mathcal {C}_n$ of n$n$ particles and describe its group of holomorphic symplectic automorphisms.
Rafael B. Andrist, Gaofeng Huang
wiley   +1 more source

Carleman estimates for semi-discrete parabolic operators with a discontinuous diffusion coefficient and application to controllability

, 2012
In the discrete setting of one-dimensional finite-differences we prove a Carleman estimate for a semi-discretization of the parabolic operator $\partial_t-\partial_x (c\partial_x)$ where the diffusion coefficient $c$ has a jump.
Nguyen, Thuy
core  

Inverse problem for a parabolic system with two components by measurements of one component

, 2008
We consider a $2\times 2$ system of parabolic equations with first and zeroth coupling and establish a Carleman estimate by extra data of only one component without data of initial values.
Benabdallah, Assia, Cristofol, Michel, Gaitan, Patricia, Yamamoto, Masahiro   +3 more
core   +1 more source

On an Empirical Likelihood Based Solution to the Approximate Bayesian Computation Problem

Statistical Analysis and Data Mining: The ASA Data Science Journal, Volume 17, Issue 5, October 2024.
ABSTRACT Approximate Bayesian computation (ABC) methods are applicable to statistical models specified by generative processes with analytically intractable likelihoods. These methods try to approximate the posterior density of a model parameter by comparing the observed data with additional process‐generated simulated data sets.
Sanjay Chaudhuri, Subhroshekhar Ghosh, Kim Cuc Pham   +2 more
wiley   +1 more source

Inverse Conductivity Problem for a Parabolic Equation using a Carlemen Estimate with one Observation

, 2007
For the heat equation in a bounded domain we give a stability result for a smooth diffusion coefficient. The key ingredients are a global Carleman-type estimate, a Poincar\'e-type estimate and an energy estimate with a single observation acting on a part
Gaitan, Patricia
core   +1 more source

On controllability of waves and geometric Carleman estimates

Séminaire Laurent Schwartz — EDP et applications, 2019
The present article is a brief summary of the paper [27], which established new Carleman and observability estimates for a general class of linear wave equations. The main features of these estimates are that (a) they apply to a fully general class of time-dependent domains, with timelike moving boundaries, (b) they apply to linear wave equations in ...
openaire   +1 more source