Multidimensional Inverse Problems for Differential EquationsSpringer, 15 Kas 2006 - 58 sayfa |
Kitabın içinden
Sayfa 1
... Section 1 considers the problem of reconstructing a two - dimensional function from its integrals over a family of ellipses with one focus 2 fixed and the other running over the points of CHAPTER Some Problems of Integral Geometry.
... Section 1 considers the problem of reconstructing a two - dimensional function from its integrals over a family of ellipses with one focus 2 fixed and the other running over the points of CHAPTER Some Problems of Integral Geometry.
Sayfa 2
... fixed at the origin and the other running over all points of the hyperplane S = 0. Only ellipsoids ob- tained by revolving an ellipse around the line joining the two foci are to be considered . It is required to determine integrals ...
... fixed at the origin and the other running over all points of the hyperplane S = 0. Only ellipsoids ob- tained by revolving an ellipse around the line joining the two foci are to be considered . It is required to determine integrals ...
Sayfa 5
... ) . Each ellipse becomes a circle of radius P and the following relation results in the limit : ( 12 ) 2п Ju ( p . 4 ) 0 Su ( p , 4 ) cosky a4 = p ̃k [ Ľkv ] e = 0 . ( k = 0,1,2 , ... ) و For each fixed value of r , these relations - 5 -
... ) . Each ellipse becomes a circle of radius P and the following relation results in the limit : ( 12 ) 2п Ju ( p . 4 ) 0 Su ( p , 4 ) cosky a4 = p ̃k [ Ľkv ] e = 0 . ( k = 0,1,2 , ... ) و For each fixed value of r , these relations - 5 -
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