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The interest of the scientific community for the existence, uniqueness and stability of solutions to PDE's is testified by the numerous works available in the literature. In particular, in some recent publications on the subject an…

Analysis of PDEs · Mathematics 2019-02-22 Daniele Casagrande , Daniele Del Santo , Martino Prizzi

We give stability estimates in the Cauchy problem for general partial differential equation of the elliptic type similar to the Helmholtz equation. We do not impose any (pseudo)convexity assumptions on the domain or the operator. These…

Analysis of PDEs · Mathematics 2018-07-04 Victor Isakov

The paper investigates stability properties of solutions of optimal control problems for semilinear parabolic partial differential equations. H\"older or Lipschitz dependence of the optimal solution on perturbations are obtained for…

Optimization and Control · Mathematics 2025-11-18 Alberto Domínguez Corella , Nicolai Jork , Vladimir M. Veliov

In this work we determine the second-order coefficient in a parabolic equation from the knowledge of a single final data. Under assumptions on the concentration of eigenvalues of the associated elliptic operator, and the initial state, we…

Analysis of PDEs · Mathematics 2020-05-19 Faouzi Triki

This paper establishes Lipschitz stability for the simultaneous recovery of a variable density coefficient and the initial displacement in a damped biharmonic wave equation. The data consist of the boundary Cauchy data for the Laplacian of…

Analysis of PDEs · Mathematics 2026-05-18 Minghui Bi , Yixian Gao

In this note we discuss the conditional stability issue for the finite dimensional Calder\'on problem for the fractional Schr\"{o}dinger equation with a finite number of measurements. More precisely, we assume that the unknown potential $q…

Analysis of PDEs · Mathematics 2018-05-03 Angkana Rüland , Eva Sincich

This paper studies stability aspects of solutions of parametric mathematical programs and generalized equations, respectively, with disjunctive constraints. We present sufficient conditions that, under some constraint qualifications…

Optimization and Control · Mathematics 2016-11-28 Helmut Gfrerer , Diethard Klatte

Using uniform global Carleman estimates for discrete elliptic and semi-discrete hyperbolic equations, we study Lipschitz and logarithmic stability for the inverse problem of recovering a potential in a semi-discrete wave equation,…

Analysis of PDEs · Mathematics 2014-09-29 Lucie Baudouin , Sylvain Ervedoza , Axel Osses

In this short paper we prove a global logarithmic stability of the Cauchy problem for H 2-solutions of an anisotropic elliptic equation in a Lip-schitz domain. The result we obtained is based on tools borrowed from the existing technics to…

Analysis of PDEs · Mathematics 2019-03-05 Mourad Choulli

The paper introduces and studies the notions of Lipschitzian and H\"olderian full stability of solutions to three-parametric variational systems described in the generalized equation formalism involving nonsmooth base mappings and partial…

Optimization and Control · Mathematics 2017-08-23 Boris S. Mordukhovich , Tran T. A. Nghia , Dat T. Pham

We extend the results of a work by L. H\"ormander in 1990 concerning the resolution of the characteristic Cauchy problem for second order wave equations with regular first order potentials. The geometrical background of this work was a…

Analysis of PDEs · Mathematics 2007-05-23 Jean-Philippe Nicolas

This paper is about Holder and Lipschitz stability estimates and uniqueness theorems for some coefficient inverse problems and associated inverse source problems for a general linear parabolic equation of the second order with variable…

Mathematical Physics · Physics 2024-01-17 Michael V. Klibanov

We obtain a uniform stability of recovering entire functions of a special form from their zeros. To this form, one can reduce the characteristic determinants of strongly regular differential operators and pencils of the first and the second…

Spectral Theory · Mathematics 2021-10-04 Sergey Buterin

In this paper we study the Cauchy problem for second order strictly hyperbolic operators when the coefficients of the principal part are not Lipschitz continuous, but only "Log-Lipschitz" with respect to all the variables. This class of…

Analysis of PDEs · Mathematics 2007-05-23 Ferruccio Colombini , Guy Metivier

This paper aims to provide various applications for second-order variational analysis of extended-real-valued piecewise liner functions recently obtained in [1]. We mainly focus here on establishing relationships between full stability of…

Optimization and Control · Mathematics 2016-08-23 B. S. Mordukhovich , M. E. Sarabi

This work is a continuation of the previous one in [{\it Optimization} (2023)], where the existence of optimal solutions and first-order necessary optimality conditions in both Pontryagin's maximum principle form and the variational form…

Optimization and Control · Mathematics 2024-10-01 Cung The Anh , Nguyen Hai Ha Giang

There is a close connection between stability and oscillation of delay differential equations. For the first-order equation $$ x^{\prime}(t)+c(t)x(\tau(t))=0,~~t\geq 0, $$ where $c$ is locally integrable of any sign, $\tau(t)\leq t$ is…

Dynamical Systems · Mathematics 2022-08-19 John Ioannis Stavroulakis , Elena Braverman

In the paper we have developed a theory of stability preserving structural transformations of systems of second-order ordinary differential equations (ODEs), i.e., the transformations which preserve the property of Lyapunov stability. The…

Dynamical Systems · Mathematics 2012-04-10 Volodymyr Makarov , Denis Dragunov

We prove a local Lipschitz stability estimate for Gel'fand-Calder\'on's inverse problem for the Schr\"odinger equation. The main novelty is that only a finite number of boundary input data is available, and those are independent of the…

Analysis of PDEs · Mathematics 2020-04-21 Giovanni S. Alberti , Matteo Santacesaria

We consider the Cauchy problem for a second-order evolution equation, in which the problem operator is the sum of two self-adjoint operators. The main feature of the problem is that one of the operators is represented in the form of the…

Numerical Analysis · Mathematics 2020-11-18 Petr N. Vabishchevich
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