Multidimensional Inverse Problems for Differential EquationsSpringer, 21 Ara 1970 - 59 sayfa |
Kitabın içinden
25 sonuçtan 1-3 arası sonuçlar
Sayfa 5
... function from its integrals over ellipses . Namely , we shall con- sider functions u ( r , ) satisfying the following conditions : is an 10. each u ( r , Y ) is a continuous function of its arguments in the disc raro , it is even in and ...
... function from its integrals over ellipses . Namely , we shall con- sider functions u ( r , ) satisfying the following conditions : is an 10. each u ( r , Y ) is a continuous function of its arguments in the disc raro , it is even in and ...
Sayfa 7
... function u ( r , ) . We now examine what properties are possessed by V , the image of the set U under the correspondence definable by ( 5 ) . Theorem 2 : The image V of U under ( 5 ) has the following properties : 1o . The functions Mv ...
... function u ( r , ) . We now examine what properties are possessed by V , the image of the set U under the correspondence definable by ( 5 ) . Theorem 2 : The image V of U under ( 5 ) has the following properties : 1o . The functions Mv ...
Sayfa 17
... function of r and a r - s ( r , s ) . In addition , = ask Qx ( s , s ) TSV ( S , S ) . Differentiating equation ( 8 ) with respect to sides of the equation by Q ( s , s ) , we obtain ( 11 ) where ( 12 ) 1 ... functions u ( r , Y ) - · - 17 -
... function of r and a r - s ( r , s ) . In addition , = ask Qx ( s , s ) TSV ( S , S ) . Differentiating equation ( 8 ) with respect to sides of the equation by Q ( s , s ) , we obtain ( 11 ) where ( 12 ) 1 ... functions u ( r , Y ) - · - 17 -
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
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