Multidimensional Inverse Problems for Differential EquationsSpringer, 21 Ara 1970 - 59 sayfa |
Kitabın içinden
22 sonuçtan 1-3 arası sonuçlar
Sayfa 43
... integral equation analogous to ( 8 ) may be derived by considering the NEUMANN problem for the same equation . Let u ( x , y , t ) be the solution to equation ( 2 ) in the half - plane y0 such that ( 14 ) u ( x , y , 0 ) = 0 , u ( x , 0 ...
... integral equation analogous to ( 8 ) may be derived by considering the NEUMANN problem for the same equation . Let u ( x , y , t ) be the solution to equation ( 2 ) in the half - plane y0 such that ( 14 ) u ( x , y , 0 ) = 0 , u ( x , 0 ...
Sayfa 44
... integral equation ∞ 1 K_ { a } [ ( x - 5 ) 2 + n2 ] 2 ) f ( 5 , n ) d ¢ ân O ( 16 ) 18 g ( x , 1 ) = = g ( x , 1 ) ... equation ( 17 ) by means of formula ( 12 ) . On inverting the FOURIER transform ( 13 ) , we arrive at the unique ...
... integral equation ∞ 1 K_ { a } [ ( x - 5 ) 2 + n2 ] 2 ) f ( 5 , n ) d ¢ ân O ( 16 ) 18 g ( x , 1 ) = = g ( x , 1 ) ... equation ( 17 ) by means of formula ( 12 ) . On inverting the FOURIER transform ( 13 ) , we arrive at the unique ...
Sayfa 47
... equation ( 8 ) is a function f ( x , xn ) satisfying the conditions 1. f ( x , x ) = 0 for Xn < α , α > 0 , n 2. f ... equation ( 8 ) can have at most one solution under these conditions . We first evaluate the integral n - 1 ( 8a ) Jn ...
... equation ( 8 ) is a function f ( x , xn ) satisfying the conditions 1. f ( x , x ) = 0 for Xn < α , α > 0 , n 2. f ... equation ( 8 ) can have at most one solution under these conditions . We first evaluate the integral n - 1 ( 8a ) Jn ...
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 |
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absolutely integrable functions Akad analytic function belong boundary conditions CAUCHY data chapter coefficients consider const continuous function coordinates corresponding cosk Denote derive determining a function differential equation Dokl domain earth's ellipses ellipsoid of revolution 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 Lavrentiev linearized inverse problem multidimensional inverse problems Nauk SSSR obtain parameters polar potential theory problem for equation problem of determining Problems for Differential R₁ R₂ right-hand side ROMANOV satisfies second kind SM,t solution to equation take FOURIER transforms telegraph equation two-parameter family unique solution uniqueness theorem unit circle variables VOLTERRA equation waves wxxx