Results 21 to 30 of about 156 (155)
Approximate controllability of the coupled degenerate system with two boundary controls
Boundary Value Problems, 2017 In this paper, we investigate the approximate controllability of the coupled system with boundary degeneracy. The control functions act on the degenerate boundary. We prove the Carleman estimate and the unique continuation of the adjoint system.
Runmei Du
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Stabilization of the weakly coupled plate equations with a locally distributed damping
Advances in Difference Equations, 2020 In this paper, we study the indirect stabilization of a system of plate equations which are weakly coupled and locally damped. By virtue of the general results due to Burq in the study of asymptotic behavior of solutions, we prove that the semigroup ...
Xianzheng Zhu
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Carleman’s and subelliptic estimates
Duke Mathematical Journal, 1988 Für einen Differentialoperator P der Ordnung m in \(\Omega \subset R^ n\) und einer glatten reellen Funktion \(\psi\) sei \(P_{\gamma}=e^{-\psi \gamma}Pe^{\psi \gamma}\) mit \(\gamma\geq 1\) gesetzt. Verf. zeigt die Ungleichungen \(\gamma^{1/(k+1)}\| u\|_{m-1,\gamma}\leq C_ K\| P_{\gamma}u\|_{L^ 2}\) und \(\gamma^{-k/(k+1)}\| u\|_{m,\gamma}\leq C_ K ...
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Carleman estimates for stratified media
Journal of Functional Analysis, 2011 Let \(\Omega=\Omega'\times (-H,H)\) be a cylinder in \(\mathbb R^n\), where \(\Omega'\) is a nonempty bounded set in \(\mathbb R^{n-1}\). Let \(S=\Omega'\times\{0\}\) be an interface where coefficients and functions may jump. The authors prove Carleman estimates for anisotropic elliptic and parabolic operators with discontinuities on \(S\).
Benabdallah, Assia +2 more
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Lipschitz stability in an inverse problem for the Korteweg-de Vries equation on a finite domain
Boundary Value Problems, 2017 In this paper, we address an inverse problem for the Korteweg-de Vries equation posed on a bounded domain with boundary conditions proposed by Colin and Ghidaglia.
Mo Chen
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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
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Carleman Estimates with a Second Large Parameter
Journal of Mathematical Analysis and Applications, 2000 Unique continuation of solutions to linear partial differential equations is of importance in many branches of applied mathematics, in particular, in control theory and inverse problems. The Carleman estimates are an important tool for proving the unique continuation for linear operators with non-analytic coefficients.
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Inverse problems for semilinear elliptic PDE with a general nonlinearity a(x,u)$a(x,u)$
Transactions of the London Mathematical Society, Volume 13, Issue 1, December 2026.Abstract This article studies the inverse problem of recovering a nonlinearity in an elliptic equation Δu+a(x,u)=0$\Delta u + a(x,u) = 0$ from boundary measurements of solutions. Previous results based on first‐order linearization achieve this under a sign condition on ∂ua(x,u)$\partial _u a(x,u)$, and results based on higher order linearization ...
David Johansson +2 more
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Quantum Time‐Marching Algorithms for Solving Linear Transport Problems Including Boundary Conditions
International Journal for Numerical Methods in Engineering, Volume 127, Issue 8, 30 April 2026.ABSTRACT This article presents the first complete application of a quantum time‐marching algorithm for simulating multidimensional linear transport phenomena with arbitrary boundaries, whereby the success probabilities are problem intrinsic. The method adapts the linear combination of unitaries algorithm to block encode the diffusive dynamics, while ...
Sergio Bengoechea +2 more
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Electronic Journal of Qualitative Theory of Differential Equations, 2018 We deal with a control problem for a coupled system of two degenerate singular parabolic equations in non-divergence form with degeneracy and singularity appearing at an interior point of the space domain. In particular, we consider the well-posedness of
Jawad Salhi
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