| Preface |
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iii | |
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Inverse Problems for Equations of Parabolic Type |
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1 | (70) |
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1 | (24) |
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The linear inverse problem: recovering a source term |
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25 | (16) |
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The linear inverse problem: the Fredholm solvability |
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41 | (13) |
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The nonlinear coefficient inverse problem: recovering a coefficient depending on x |
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54 | (6) |
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The linear inverse problem: recovering the evolution of a source term |
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60 | (11) |
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Inverse Problems for Equations of Hyperbolic Type |
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71 | (52) |
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Inverse problems for x-hyperbolic systems |
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71 | (17) |
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Inverse problems for t-hyperbolic systems |
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88 | (18) |
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Inverse problems for hyperbolic equations of the second order |
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106 | (17) |
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Inverse Problems for Equations of the Elliptic Type |
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123 | (80) |
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Introduction to inverse problems in potential theory |
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123 | (4) |
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Necessary and sufficient conditions for the equality of exterior magnetic potentials |
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127 | (12) |
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The exterior inverse problem for the volume potential with variable density for bodies with a ``star-shaped'' intersection |
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139 | (13) |
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Integral stability estimates for the inverse problem of the exterior potential with constant density |
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152 | (14) |
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Uniqueness theorems for the harmonic potential of ``non-star-shaped'' bodies with variable density |
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166 | (5) |
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The exterior contact inverse problem for the magnetic potential with variable density of constant sign |
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171 | (8) |
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Integral equation for finding the density of a given body via its exterior potential |
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179 | (13) |
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Uniqueness of the inverse problem solution for the simple layer potential |
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192 | (5) |
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Stability in inverse problems for the potential of a simple layer in the space Rn, n≥3 |
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197 | (6) |
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Inverse Problems in Dynamics of Viscous Incompressible Fluid |
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203 | (96) |
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203 | (6) |
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Nonstationary linearized system of Navier-Stokes equations: the final overdetermination |
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209 | (12) |
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Nonstationary linearized system of Navier-Stokes equations: the integral overdetermination |
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221 | (9) |
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Nonstationary nonlinear system of Navier-Stokes equations: three-dimensional flow |
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230 | (18) |
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Nonstationary nonlinear system of Navier-Stokes equations: two-dimensional flow |
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248 | (6) |
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Nonstationary nonlinear system of Navier-Stokes equations: the integral overdetermination |
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254 | (12) |
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Nonstationary linearized system of Navier-Stokes equations: adopting a linearization via recovering a coefficient |
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266 | (15) |
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Nonstationary linearized system of Navier-Stokes equations: the combined recovery of two coefficients |
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281 | (18) |
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Some Topics from Functional Analysis and Operator Theory |
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299 | (76) |
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The basic notions of functional analysis and operator theory |
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299 | (30) |
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Linear differential equations of the first order in Banach spaces |
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329 | (13) |
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Linear differential equations of the second order in Banach spaces |
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342 | (12) |
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Differential equations with varying operator coefficients |
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354 | (10) |
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Boundary value problems for elliptic differential equations of the second order |
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364 | (11) |
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Abstract Inverse Problems for First Order Equations and Their Applications in Mathematical Physics |
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375 | (114) |
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Equations of mathematical physics and abstract problems |
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375 | (5) |
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The linear inverse problem with smoothing overdetermination: the basic elements of the theory |
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380 | (14) |
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Nonlinear inverse problems with smoothing overdetermination: solvability |
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394 | (12) |
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Inverse problems with smoothing overdetermination: smoothness of solution |
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406 | (8) |
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Inverse problems with singular overdetermination: semilinear equations with constant operation in the principal part |
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414 | (24) |
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Inverse problems with smoothing overdetermination: quasilinear parabolic equations |
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438 | (11) |
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Inverse problems with singular overdetermination: semilinear parabolic equations |
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449 | (9) |
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Inverse problems with smoothing overdetermination: semilinear hyperbolic equations |
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458 | (11) |
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Inverse problems with singular overdetermination: semilinear hyperbolic equations |
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469 | (7) |
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Inverse problems with smoothing overdetermination: semilinear hyperbolic equations and operators with fixed domain |
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476 | (13) |
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Two-Point Inverse Problems for First Order Equations |
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489 | (34) |
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Two-point inverse problems |
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489 | (12) |
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Inverse problems with self-adjoint operator and scalar function Φ |
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501 | (13) |
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Two-point inverse problems in Banach lattices |
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514 | (9) |
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Inverse Problems for Equations of Second Order |
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523 | (52) |
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Cauchy problem for semilinear hyperbolic equations |
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523 | (14) |
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Two-point inverse problems for equations of hyperbolic type |
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537 | (20) |
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Two-point inverse problems for equations of the elliptic type |
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557 | (18) |
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Applications of the Theory of Abstract Inverse Problems to Partial Differential Equations |
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575 | (70) |
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Symmetric hyperbolic systems |
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575 | (9) |
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Second order equations of hyperbolic type |
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584 | (7) |
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The system of equations from elasticity theory |
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591 | (6) |
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Equations of heat transfer |
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597 | (10) |
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Equations of neutron transport |
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607 | (7) |
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Linearized Bolzman equation |
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614 | (14) |
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The system of Navier-Stokes equations |
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628 | (8) |
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The system of Maxwell equations |
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636 | (9) |
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645 | (16) |
| References |
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661 | (44) |
| Index |
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705 | |
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