Inverse Problems for Partial Differential Equations
Springer Science & Business Media, 20 Kas 1997 - 286 sayfa
This book describes the contemporary state of the theory and some numerical aspects of inverse problems in partial differential equations. The topic is of sub stantial and growing interest for many scientists and engineers, and accordingly to graduate students in these areas. Mathematically, these problems are relatively new and quite challenging due to the lack of conventional stability and to nonlinearity and nonconvexity. Applications include recovery of inclusions from anomalies of their gravitational fields; reconstruction of the interior of the human body from exterior electrical, ultrasonic, and magnetic measurements, recovery of interior structural parameters of detail of machines and of the underground from similar data (non-destructive evaluation); and locating flying or navigated objects from their acoustic or electromagnetic fields. Currently, there are hundreds of publica tions containing new and interesting results. A purpose of the book is to collect and present many of them in a readable and informative form. Rigorous proofs are presented whenever they are relatively short and can be demonstrated by quite general mathematical techniques. Also, we prefer to present results that from our point of view contain fresh and promising ideas. In some cases there is no com plete mathematical theory, so we give only available results. We do not assume that a reader possesses an enormous mathematical technique. In fact, a moderate knowledge of partial differential equations, of the Fourier transform, and of basic functional analysis will suffice.
Diğer baskılar - Tümünü görüntüle
a₁ a₂ algorithms analytic assume assumptions boundary condition boundary measurements boundary value problem bounded c₁ Cauchy data Cauchy problem coefficients conclude consider constant continuous convergence convex Corollary D₁ D₂ data g defined differential equation Dirichlet data Dirichlet problem Dirichlet-to-Neumann map div(a domain eigenvalues elliptic equation elliptic operator equation 2.0 formula function given gravimetry Green's formula harmonic heat equation Helmholtz equation hyperbolic equation hyperbolic problem ill-posed problems inequality integral equation integral geometry inverse conductivity problem inverse problem Isakov lateral boundary data Lemma linear Lipschitz maximum principle method Neumann data Neumann-to-Dirichlet nonlinear norm observe obtain operator parabolic equation parabolic problem proof is complete proof of Theorem Prove uniqueness Radon transform regularization respect right side satisfies scattering Section smooth solution solves space stability estimate u₁ uniquely determined uniqueness results v₁ ΘΩ
Sayfa xi - This book describes the contemporary state of the theory and some numerical aspects of inverse problems in partial differential equations. The topic is of substantial and growing interest for many scientists