Multidimensional Inverse Problems for Differential EquationsSpringer, 15 Kas 2006 - 58 sayfa |
Kitabın içinden
Sayfa 1
... formulas for them and the set of functions for which these formulas are valid . The latter is related to the question of existence of a solution . Section 1 considers the problem of reconstructing a two - dimensional function from its ...
... formulas for them and the set of functions for which these formulas are valid . The latter is related to the question of existence of a solution . Section 1 considers the problem of reconstructing a two - dimensional function from its ...
Sayfa 2
... formula is obtained for the problem of determining a function from its mean values over circles . Although , as we have indicated already , uniqueness has been proved before and a basic algorithm exists for constructing the required ...
... formula is obtained for the problem of determining a function from its mean values over circles . Although , as we have indicated already , uniqueness has been proved before and a basic algorithm exists for constructing the required ...
Sayfa 3
... formulas u ( x , s ) . ( r , ) ( 3 ) x = r Cos = r > sin · The equation of an ellipse in polar coordinates is ( 4 ) r = p ( 1 ... Formula ( 2 ) then becomes 2π , p = 1⁄2 ( 1 − c2 ) . - ( 5 ) u ( r cos , r sin ) d = v ( p , e ) v ( p , c ) ...
... formulas u ( x , s ) . ( r , ) ( 3 ) x = r Cos = r > sin · The equation of an ellipse in polar coordinates is ( 4 ) r = p ( 1 ... Formula ( 2 ) then becomes 2π , p = 1⁄2 ( 1 − c2 ) . - ( 5 ) u ( r cos , r sin ) d = v ( p , e ) v ( p , c ) ...
Sayfa 4
... formula ( 4 ) when calculating an ellipse with parameters p and ε r . P , E Sp , denotes Applying the operator L repeatedly to the resultant equation ( 7 ) s u ( x , s ) xd Lv = S P , ε and denoting by Lk the k - fold iteration of L ...
... formula ( 4 ) when calculating an ellipse with parameters p and ε r . P , E Sp , denotes Applying the operator L repeatedly to the resultant equation ( 7 ) s u ( x , s ) xd Lv = S P , ε and denoting by Lk the k - fold iteration of L ...
Sayfa 6
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İçindekiler
1 | |
Linearized Inverse Dynamic Problem for the Telegraph | 22 |
Derivation of a Nonlinear Differential Equation for | 31 |
CHAPTER 4 | 39 |
CHAPTER 5 | 52 |
Diğer baskılar - Tümünü görüntüle
Multidimensional Inverse Problems for Differential Equations M. M. Lavrentiev,V. G. Romanov,V. G. Vasiliev Metin Parçacığı görünümü - 1970 |
Multidimensional Inverse Problems for Differential Equations M. M. Lavrentiev,V. G. Romanov,V. G. Vasiliev Metin Parçacığı görünümü - 1970 |
Sık kullanılan terimler ve kelime öbekleri
absolutely integrable functions analytic function belong boundary conditions CAUCHY data chapter consider const construct continuous function corresponding Denote derive determining a function differential equation domain earth's ellipses ellipsoid of revolution exists expression family of curves following theorem function f(x,y functions u(r fundamental solution given GREEN'S function half-plane half-space HÖLDER condition hyperplane inequality 16 initial and boundary integral equation integral geometry integral-geometric problem Introduce the notation Inverse Kinematic Inverse Kinematic Problem inversion formula kernel L₁(D linearized inverse problem M₁ mean values multidimensional inverse problems obtain operator L defined parameters polar problem for equation problem of determining Q₂ R₂ relations right-hand side second kind sense of HADAMARD SM,t solution to equation space STURM-LIOUVILLE equations take FOURIER transforms telegraph equation travel-times two-parameter family u₁ M,M,t unique solution uniqueness theorem unit circle values over spheres variables VOLTERRA equation ду