Multidimensional Inverse Problems for Differential EquationsSpringer, 21 Ara 1970 - 59 sayfa |
Kitabın içinden
8 sonuçtan 1-3 arası sonuçlar
Sayfa 9
... Introduce spherical coordinates for y and S by the formulas ( 21 ) , y1 = S r51 = r5n + 1 ( 1 = 1,2 , ... , n ) where 51 ( 1 ( 1 = = 1,2 , ... , n + 1 ) are the direction cosines of the radius vector r in ( y , s ) -space . The equation ...
... Introduce spherical coordinates for y and S by the formulas ( 21 ) , y1 = S r51 = r5n + 1 ( 1 = 1,2 , ... , n ) where 51 ( 1 ( 1 = = 1,2 , ... , n + 1 ) are the direction cosines of the radius vector r in ( y , s ) -space . The equation ...
Sayfa 11
... Introduce the operator L defined by a ( 6 ) Lv = θε fv ( 200 ) v ( z , e ) Z and apply it to ( 4 ) . Its validity is justified by the HOLDER condition for the function u ( r , ) . Indeed , ( 6a ) p pf ( ε , ε cos ) a dz = θε Ꮓ Sp ...
... Introduce the operator L defined by a ( 6 ) Lv = θε fv ( 200 ) v ( z , e ) Z and apply it to ( 4 ) . Its validity is justified by the HOLDER condition for the function u ( r , ) . Indeed , ( 6a ) p pf ( ε , ε cos ) a dz = θε Ꮓ Sp ...
Sayfa 42
... Introduce the notation | G ( w , λ ) | < απ 2,2 2 a - λ + w t = n - Ꭹ . p2 = a ( 10a ) 1 F1 ( w , t ) = F ( w2t + y 1 ) y1p Q1 ( w , p ) e = Q ( w , 11 √ 2 2 31 p , = F ( w , t ) + 1F12 ( wet ) , 11 1F12 > = Q11 ( w , p ) + 1Q12 ( w ...
... Introduce the notation | G ( w , λ ) | < απ 2,2 2 a - λ + w t = n - Ꭹ . p2 = a ( 10a ) 1 F1 ( w , t ) = F ( w2t + y 1 ) y1p Q1 ( w , p ) e = Q ( w , 11 √ 2 2 31 p , = F ( w , t ) + 1F12 ( wet ) , 11 1F12 > = Q11 ( w , p ) + 1Q12 ( w ...
İçindekiler
CHAPTER | 1 |
Problem of Determining a Function inside a Circle from | 13 |
On the Problem of Determining a Function from Its Mean | 19 |
Telif Hakkı | |
4 diğer bölüm gösterilmiyor
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 arbitrary belong boundary conditions CAUCHY data chapter consider const 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 u(r fundamental solution given GREEN'S function half-plane half-space HOLDER condition hyperplane inequality 16 initial and boundary integral equation integral geometry integral-geometric problem Introduce the notation inverse kinematic inverse kinematic problem inverse problem inversion formula kernel L₁ linearized inverse problem M₁ mean values multidimensional inverse problems n₁ obtain operator L defined parameters polar problem for equation problem of determining Q₂ R₁ R₂ relations right-hand side second kind SM,t solution to equation 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 waves wxxx θε ду эф