Stability estimates for ill-posed cauchy problems involving hyperbolic equations and inequalities
From MaRDI portal
Publication:4291831
DOI10.1080/00036819308840186zbMath0795.35134OpenAlexW2036661666WikidataQ58285281 ScholiaQ58285281MaRDI QIDQ4291831
Mohammad A. Kazemi, Michael V. Klibanov
Publication date: 14 September 1994
Published in: Applicable Analysis (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1080/00036819308840186
Ill-posed problems for PDEs (35R25) Inverse problems for PDEs (35R30) A priori estimates in context of PDEs (35B45) Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs (35B30) Unilateral problems for linear hyperbolic equations and variational inequalities with linear hyperbolic operators (35L85)
Related Items
An inverse stability result for non-compactly supported potentials by one arbitrary lateral Neumann observation, Stabilization of the wave equations with potential and indefinite damping, A Lipschitz stable reconstruction formula for the inverse problem for the wave equation, Carleman estimates for second-order hyperbolic systems in anisotropic cases and applications. Part I: Carleman estimates, Carleman estimates for second-order hyperbolic systems in anisotropic cases and applications. Part II: an inverse source problem, Stability estimate in determination of a coefficient in transmission wave equation by boundary observation, Convergence of the wave equation damped on the interior to the one damped on the boundary, Carleman estimates for the Schrödinger equation and applications to an inverse problem and an observability inequality, State observation problem for general time reversible system and applications, A Carleman estimate and an energy method for a first-order symmetric hyperbolic system, Exact local controllability for the equations of viscous gas dynamics, Observability inequalities by internal observation and their applications, A Carleman estimate for the linear magnetoelastic waves system and an inverse source problem in a bounded conductive medium, Decay of semilinear damped wave equations: cases without geometric control condition, Uniqueness and Lipschitz stability in electrical impedance tomography with finitely many electrodes, An inverse space-dependent source problem for hyperbolic equations and the Lipschitz-like convergence of the quasi-reversibility method, Global Uniqueness and Lipschitz-Stability for the Inverse Robin Transmission Problem, On a stability estimate for a solution to an~inverse problem for a hyperbolic equation, Carleman estimate for wave equations coupled with the second order terms, Uniqueness, Lipschitz Stability, and Reconstruction for the Inverse Optical Tomography Problem, Uniqueness, stability and global convergence for a discrete inverse elliptic Robin transmission problem, Numerical solution of the problem of computational time reversal in a quadrant, Uniqueness and stability in determining the speed of propagation of second-order hyperbolic equation with variable coefficients, Logarithmic stability in determination of a coefficient in an acoustic equation by arbitrary boundary observation, Global uniqueness and stability for an inverse wave source problem for less regular data, Stability estimate in the determination of a time-dependent coefficient for hyperbolic equation by partial Dirichlet-to-Neumann map, Carleman estimates for the non-stationary Lamé system and the application to an inverse problem, Lipschitz stability in determining density and two Lamé coefficients, Monotonicity-Based Inversion of the Fractional Schrödinger Equation II. General Potentials and Stability, Logarithmic stability in the dynamical inverse problem for the Schrödinger equation by arbitrary boundary observation, Determination of a source term in a partial differential equation arising in finance, Lipschitz stability of an inverse problem for an acoustic equation, New realization of the pseudoconvexity and its application to an inverse problem, Inverse problem for a parabolic system with two components by measurements of one component, An inverse problem and an observability inequality for the Lamé system with stress boundary condition, Biography of Michael V. Klibanov Professor, Ph.D. and Doctor of Science in Physics and Mathematics and an outstanding expert in inverse problems, Uniqueness and stability in multidimensional hyperbolic inverse problems, Finite-dimensional boundary uniform stabilization of the Boussinesq system in Besov spaces by critical use of Carleman estimate-based inverse theory, Determination of point sources in vibrating plate by boundary measurements, Lipschitz stability in an inverse problem for a hyperbolic equation with a finite set of boundary data, A new version of the quasi-reversibility method for the thermoacoustic tomography and a coefficient inverse problem, Stability of an inverse problem for the discrete wave equation and convergence results, Carleman estimates for the regularization of ill-posed Cauchy problems, Some regularization methods for a thermoacoustic inverse problem
Cites Work
- Unnamed Item
- Uniform exponential energy decay of wave equations in a bounded region with \(L_ 2(0,\infty;L_ 2(\Gamma))\)-feedback control in the Dirichlet boundary conditions
- Uniform stabilization of the wave equation with Dirichlet or Neumann feedback control without geometrical conditions
- Newton-Kantorovich method for three-dimensional potential inverse scattering problem and stability of the hyperbolic Cauchy problem with time-dependent data