Multidimensional Inverse Problems for Differential EquationsSpringer, 21 Ara 1970 - 59 sayfa |
Kitabın içinden
11 sonuçtan 1-3 arası sonuçlar
Sayfa 6
... hence we can find its integrals along all ellipses lying in this disc . This means that if we prescribe the function v ( p , ε ) in an arbitrarily small strip 0 ≤ ε ≤ 8 , ΕΣ δ we determine it completely for δε < 1. This implies in ...
... hence we can find its integrals along all ellipses lying in this disc . This means that if we prescribe the function v ( p , ε ) in an arbitrarily small strip 0 ≤ ε ≤ 8 , ΕΣ δ we determine it completely for δε < 1. This implies in ...
Sayfa 42
... Hence it follows that each of the equations in ( 11 ) has just one solution and it may be expressed by the formula [ 26 ] : n ( -1 ) n ( ) n + 1 ( 12 ) F11 ( w , z ) = lim n Q11 ( w , 2 ) ap ( 1 = 1,2 ) . n + ∞ n ! Further , it is ...
... Hence it follows that each of the equations in ( 11 ) has just one solution and it may be expressed by the formula [ 26 ] : n ( -1 ) n ( ) n + 1 ( 12 ) F11 ( w , z ) = lim n Q11 ( w , 2 ) ap ( 1 = 1,2 ) . n + ∞ n ! Further , it is ...
Sayfa 43
... boundary of the half - plane . Hence , N ( x , y ; E , n ) is the GREEN'S function of second kind for the half - plane . The solution to equation ( 4 ) can thus be represented in the following form : ∞ x ( x , y , x ) = - 43 -
... boundary of the half - plane . Hence , N ( x , y ; E , n ) is the GREEN'S function of second kind for the half - plane . The solution to equation ( 4 ) can thus be represented in the following form : ∞ x ( x , y , x ) = - 43 -
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