Multidimensional Inverse Problems for Differential EquationsSpringer, 15 Kas 2006 - 58 sayfa |
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25 sonuçtan 1-5 arası sonuçlar
Sayfa 2
... function of n variables from its inte- grals over ellipsoids of revolution ... u ( x , s ) = u ( x1 , x2 , ... , x , s ) are prescribed on a X2 • • n ... r ( x , s , 0,0 ) + r ( x , s , x ° , 0 ) = t where r ( x , s , 0,0 ) and the foci ...
... function of n variables from its inte- grals over ellipsoids of revolution ... u ( x , s ) = u ( x1 , x2 , ... , x , s ) are prescribed on a X2 • • n ... r ( x , s , 0,0 ) + r ( x , s , x ° , 0 ) = t where r ( x , s , 0,0 ) and the foci ...
Sayfa 3
... function of S vanishing at the origin . The idea of the proof of the theorem is to find all moments of To this end , it is convenient to go over to polar coordinates related to the cartesian coordinates ( x , s ) by the formulas u ... ( r , ) ( ...
... function of S vanishing at the origin . The idea of the proof of the theorem is to find all moments of To this end , it is convenient to go over to polar coordinates related to the cartesian coordinates ( x , s ) by the formulas u ... ( r , ) ( ...
Sayfa 4
... u ( r cos❤ , r sin❤ ) dr 2π u ( rp cosy , гp sin ) гр cos4 14 = Su ( x , 8 ) x14 S Ρ , ε The subscripts p and Z on ... function of s , it is uniquely de- termined by these moments . In other words , if a solution to equation ( 4 ) exists , ...
... u ( r cos❤ , r sin❤ ) dr 2π u ( rp cosy , гp sin ) гр cos4 14 = Su ( x , 8 ) x14 S Ρ , ε The subscripts p and Z on ... function of s , it is uniquely de- termined by these moments . In other words , if a solution to equation ( 4 ) exists , ...
Sayfa 5
... u ( r , ) satisfying the following conditions : is a continuous function of its arguments in the disc rsr it is even in Ŷ and u ( 0,9 ) = 0. Here r 1o . each u ( r , 4 ) > O arbitrary positive number . 2o . In a neighborhood of the ...
... u ( r , ) satisfying the following conditions : is a continuous function of its arguments in the disc rsr it is even in Ŷ and u ( 0,9 ) = 0. Here r 1o . each u ( r , 4 ) > O arbitrary positive number . 2o . In a neighborhood of the ...
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