Multidimensional Inverse Problems for Differential EquationsSpringer, 21 Ara 1970 - 59 sayfa |
Kitabın içinden
9 sonuçtan 1-3 arası sonuçlar
Sayfa 12
... constant . The equation has no other eigenfunctions . Note however that the boundedness of u ( r , ) together with ( 4 ) implies the boundedness of all V1 ( p , ε ) and so the solution we seek for ( 9 ) has to be bounded . But since for ...
... constant . The equation has no other eigenfunctions . Note however that the boundedness of u ( r , ) together with ( 4 ) implies the boundedness of all V1 ( p , ε ) and so the solution we seek for ( 9 ) has to be bounded . But since for ...
Sayfa 52
... const . , P = ( , n ) , b ( P ) = 0 for n < Y1 , and let the domain D be the half - plane n≥0 . Under these conditions , equation ( 4 ) becomes ( 5 ) ∞了] ] b ( 5 , n ) [ K ( ar1 ) -K_ ( ar2 ) ] [ K ( arz ) -K ( ar1 ) ] d ¢ ân = f ...
... const . , P = ( , n ) , b ( P ) = 0 for n < Y1 , and let the domain D be the half - plane n≥0 . Under these conditions , equation ( 4 ) becomes ( 5 ) ∞了] ] b ( 5 , n ) [ K ( ar1 ) -K_ ( ar2 ) ] [ K ( arz ) -K ( ar1 ) ] d ¢ ân = f ...
Sayfa 53
... const > 0 . [ ( E - x2 ) 2 + ( n + 1 ) 2 ] 2 , We impose on the right - hand side f ( x1 , x2 ) of integral equation ( 5 ) the single requirement that the solution b ( 5 , n ) of the equation belong to L1 ( D ) . We take FOURIER ...
... const > 0 . [ ( E - x2 ) 2 + ( n + 1 ) 2 ] 2 , We impose on the right - hand side f ( x1 , x2 ) of integral equation ( 5 ) the single requirement that the solution b ( 5 , n ) of the equation belong to L1 ( D ) . We take FOURIER ...
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