Multidimensional Inverse Problems for Differential EquationsSpringer, 21 Ara 1970 - 59 sayfa |
Kitabın içinden
7 sonuçtan 1-3 arası sonuçlar
Sayfa 47
... ( x , xn ) satisfying the conditions 1. f ( x , x ) = 0 n for Xn < α , a > 0 , 2. f ( x , x ) € L1 ( D ) . 1 Let us show that equation ( 8 ) can have at most one solution under these conditions . We first evaluate the integral n - 1 00 ...
... ( x , xn ) satisfying the conditions 1. f ( x , x ) = 0 n for Xn < α , a > 0 , 2. f ( x , x ) € L1 ( D ) . 1 Let us show that equation ( 8 ) can have at most one solution under these conditions . We first evaluate the integral n - 1 00 ...
Sayfa 48
... ( x , λ ) e ω 2 ... n - 1 n - 1 -1 [ wzx k = 1 wxxx n - 1 dx -1 Σ wxxx [ J ... ] 8 J ... Je k = 1 f ( x , xn ) e -∞ > dx By the first assumption , f ( x , xn ) vanishes for x < a and so F ( w ) a . Therefore equation ( 11 ) has the ...
... ( x , λ ) e ω 2 ... n - 1 n - 1 -1 [ wzx k = 1 wxxx n - 1 dx -1 Σ wxxx [ J ... ] 8 J ... Je k = 1 f ( x , xn ) e -∞ > dx By the first assumption , f ( x , xn ) vanishes for x < a and so F ( w ) a . Therefore equation ( 11 ) has the ...
Sayfa 49
... ( x , n , n ) , ' n - is the GREEN'S function of second kind for the half - space D. By using it we can represent the solution to ( 4 ) by √ ( x , x1 ) ( 13 ) If we set xn = -2 ( m1 ( x , 1 ) Q2 ( x , x ̧¡5,0 ) d5 { my ( x , x ) S + N ( X ) ...
... ( x , n , n ) , ' n - is the GREEN'S function of second kind for the half - space D. By using it we can represent the solution to ( 4 ) by √ ( x , x1 ) ( 13 ) If we set xn = -2 ( m1 ( x , 1 ) Q2 ( x , x ̧¡5,0 ) d5 { my ( x , x ) S + N ( X ) ...
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