Multidimensional Inverse Problems for Differential EquationsSpringer, 21 Ara 1970 - 59 sayfa |
Kitabın içinden
23 sonuçtan 1-3 arası sonuçlar
Sayfa 10
... given in polar Ρ , ε ( 1 ) r = pf ( e , e cos ) , where f ( e , n ) is an analytic function of Ε and n in an arbitrary small neighborhood of the origin such that f ( 0,0 ) # 0 and a f ( 0,0 ) 0. Let the integrals an ( 2 ) Soc ♢ ( e , ɛ ...
... given in polar Ρ , ε ( 1 ) r = pf ( e , e cos ) , where f ( e , n ) is an analytic function of Ε and n in an arbitrary small neighborhood of the origin such that f ( 0,0 ) # 0 and a f ( 0,0 ) 0. Let the integrals an ( 2 ) Soc ♢ ( e , ɛ ...
Sayfa 13
... given by P , E equation ( 4 ) of Sec.1 , we have ( 10a ) s ( 1 - e cos ) u ( r , Y ) a = 0 for any р and Sp , ε < 1. But this means that equation ( 2 ) has corres- v ( p , ε ) = 0 not only the trivial solution but also the nontrivial ...
... given by P , E equation ( 4 ) of Sec.1 , we have ( 10a ) s ( 1 - e cos ) u ( r , Y ) a = 0 for any р and Sp , ε < 1. But this means that equation ( 2 ) has corres- v ( p , ε ) = 0 not only the trivial solution but also the nontrivial ...
Sayfa 28
... given by ( 1 ) O u ( M , M , t ) == s ( t - r ( M , M ) ) O 2π г ( M , M In this formula r ( M , M ) is the distance between the points M and M. O The solution to equation ( 9 ) of Sec . 1 under corresponding initial and boundary ...
... given by ( 1 ) O u ( M , M , t ) == s ( t - r ( M , M ) ) O 2π г ( M , M In this formula r ( M , M ) is the distance between the points M and M. O The solution to equation ( 9 ) of Sec . 1 under corresponding initial and boundary ...
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