Multidimensional Inverse Problems for Differential EquationsM. M. Lavrentiev, Mikhail Mikhailovich Lavrent£ev, Vladimir Gavrilovich Romanov, V. G. Romanov, V. G. Vasiliev Springer, 21 Ara 1970 - 59 sayfa |
Kitabın içinden
3 sonuçtan 1-3 arası sonuçlar
Sayfa 11
... substituting it in formula ( 2 ) , we obtain ( 3 ) v ( p , ε ) = ∞ Σ k = 0 [ ekak ( c ) Vk ( P , ) , where ( 4 ) Vk ( p , ε ) = ( 5 ) ax ( ε ) = k ! k an | n = o Sulr , 4 ) cost 414 , Sp , ε k эф If we are able to determine the ...
... substituting it in formula ( 2 ) , we obtain ( 3 ) v ( p , ε ) = ∞ Σ k = 0 [ ekak ( c ) Vk ( P , ) , where ( 4 ) Vk ( p , ε ) = ( 5 ) ax ( ε ) = k ! k an | n = o Sulr , 4 ) cost 414 , Sp , ε k эф If we are able to determine the ...
Sayfa 42
... Substituting the last inequality into ( 9 ) , we finally obtain ( 10 ) Introduce the notation | G ( w , x ) | < απ 2.2 + ო 2 2 t = n - y1 p2 = a2x 2.2 + 3 2 , , F1 ( w , t ) = F ( w , t + y 1 ) = F11 ( w , t ) + 1F12 ( w , t ) , ( 10a ) ...
... Substituting the last inequality into ( 9 ) , we finally obtain ( 10 ) Introduce the notation | G ( w , x ) | < απ 2.2 + ო 2 2 t = n - y1 p2 = a2x 2.2 + 3 2 , , F1 ( w , t ) = F ( w , t + y 1 ) = F11 ( w , t ) + 1F12 ( w , t ) , ( 10a ) ...
Sayfa 54
... Substituting ( 7 ) in ( 6 ) , we obtain ( 8 ) ( 9 ) 00 So την e r ( u , n ) dn = F2 ( u , v ) , b ( 5 , n ) e -1ud . ¥ 1 = ( o ( con ) r ( u , n ) = Since b ( , n ) is by hypothesis an absolutely integrable function , r ( u , n ) is ...
... Substituting ( 7 ) in ( 6 ) , we obtain ( 8 ) ( 9 ) 00 So την e r ( u , n ) dn = F2 ( u , v ) , b ( 5 , n ) e -1ud . ¥ 1 = ( o ( con ) r ( u , n ) = Since b ( , n ) is by hypothesis an absolutely integrable function , r ( u , n ) is ...
İçindekiler
Generalization to Analytic Curves | 10 |
On the Problem of Determining a Function from Its Mean | 19 |
Two Formulations of the Linearized Inverse Problem | 28 |
Telif Hakkı | |
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Diğer baskılar - Tümünü görüntüle
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 Akad belong boundary conditions CAUCHY data chapter coefficients consider const continuous function corresponding cosy Denote derive determining a function differential equation Dokl domain earth's ellipses ellipsoid of revolution exists expression family of curves following theorem function u(r fundamental solution given GREEN'S function half-plane half-space HÖLDER condition hyperplane inequality 18 integral equation integral geometry integral-geometric problem Introduce the notation inverse kinematic inverse kinematic problem inversion formula kernel linearized inverse problem mean values multidimensional inverse problems Nauk SSSR obtain operator L defined parameters polar potential theory problem for equation problem of determining Problems for Differential R₁ R₂ right-hand side ROMANOV satisfies second kind solution to equation STURM-LIOUVILLE equations take FOURIER transforms telegraph equation travel-times two-parameter family unique solution uniqueness theorem unit circle values over spheres variables VOLTERRA equation waves wxxx