Multidimensional Inverse Problems for Differential EquationsSpringer, 21 Ara 1970 - 59 sayfa |
Kitabın içinden
3 sonuçtan 1-3 arası sonuçlar
Sayfa 7
... ( 16 ) 00 Σ max│Mxv | ε = 0 av = k = 0 p is convergent . 30. The function u ( r , ) constructed for v ( p , ε ) from formula ( 15 ) satisfies the HOLDER condition , ( 17 ) ur , Ar " , ( u > 0 ) . 40. Each v ( p , ɛ ) satisfies the inequality ...
... ( 16 ) 00 Σ max│Mxv | ε = 0 av = k = 0 p is convergent . 30. The function u ( r , ) constructed for v ( p , ε ) from formula ( 15 ) satisfies the HOLDER condition , ( 17 ) ur , Ar " , ( u > 0 ) . 40. Each v ( p , ɛ ) satisfies the inequality ...
Sayfa 18
... ( 16 ) эф | v ( p , a ) | ≤ av • Σ j = 1 √1 + ( r dr ar P The fulfillment of the first and second conditions follows from ( 13 ) and ( 14 ) . To prove the validity of inequality ( 16 ) , we consider the inversion formula for the given ...
... ( 16 ) эф | v ( p , a ) | ≤ av • Σ j = 1 √1 + ( r dr ar P The fulfillment of the first and second conditions follows from ( 13 ) and ( 14 ) . To prove the validity of inequality ( 16 ) , we consider the inversion formula for the given ...
Sayfa 19
... inequality ( 16 ) . This implies that w ( p , a ) = 0 , or in other words , ( p , a ) = v ( p , a ) . But this means that to each v ( p , a ) E V we have constructed a solution to equation ( 2 ) . By Theorem 5 , it is unique ...
... inequality ( 16 ) . This implies that w ( p , a ) = 0 , or in other words , ( p , a ) = v ( p , a ) . But this means that to each v ( p , a ) E V we have constructed a solution to equation ( 2 ) . By Theorem 5 , it is unique ...
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