Multidimensional Inverse Problems for Differential EquationsSpringer, 21 Ara 1970 - 59 sayfa |
Kitabın içinden
19 sonuçtan 1-3 arası sonuçlar
Sayfa 4
... applying it are substantiated by the following sequence of equations : a Lv = p де dz 2π u ( r2cos , r2 sind rz u ( r2 cos , sin ) rz dz Z θε } u ( r cos , r sin ) dr r ( 6a ) = p = p a θε 2π 2π 2π } 14 аф } u ( rp cosy , sin ) r ...
... applying it are substantiated by the following sequence of equations : a Lv = p де dz 2π u ( r2cos , r2 sind rz u ( r2 cos , sin ) rz dz Z θε } u ( r cos , r sin ) dr r ( 6a ) = p = p a θε 2π 2π 2π } 14 аф } u ( rp cosy , sin ) r ...
Sayfa 12
... Apply L to ( 3 ) and use formula ( 7 ) for Lv . This results in Lv ( 8 ) = ∞ do d ( ε ) v ( p , ε ) + [ [ ¢ k - 1d ( e ) Vk ( P‚¤ ) + l ( ε ) O 。( e ) } } vo ( O ) 1 k = 1 dz + Ε مرد dz , V。( 2 , c ) # + 1 ck = 1 , ( c ) & vx ( D , c ) ...
... Apply L to ( 3 ) and use formula ( 7 ) for Lv . This results in Lv ( 8 ) = ∞ do d ( ε ) v ( p , ε ) + [ [ ¢ k - 1d ( e ) Vk ( P‚¤ ) + l ( ε ) O 。( e ) } } vo ( O ) 1 k = 1 dz + Ε مرد dz , V。( 2 , c ) # + 1 ck = 1 , ( c ) & vx ( D , c ) ...
Sayfa 20
... Applying to ( 1 ) the operator L defined by ( 2 ) a ах Lv = xv ( x , r ) + r } x / pv ( x , p ) dp = x Juc u ( x + r ... application of L to v ( x , r ) . Then in a similar way , we have 2 п u ( x + r.cos , resin ) ( x + r.cos ) kay ( 3 ) ...
... Applying to ( 1 ) the operator L defined by ( 2 ) a ах Lv = xv ( x , r ) + r } x / pv ( x , p ) dp = x Juc u ( x + r ... application of L to v ( x , r ) . Then in a similar way , we have 2 п u ( x + r.cos , resin ) ( x + r.cos ) kay ( 3 ) ...
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 |
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