Multidimensional Inverse Problems for Differential EquationsM. M. Lavrentiev, Mikhail Mikhailovich Lavrent£ev, Vladimir Gavrilovich Romanov, V. G. Romanov, V. G. Vasiliev Springer, 21 Ara 1970 - 59 sayfa |
Kitabın içinden
14 sonuçtan 1-3 arası sonuçlar
Sayfa 6
... relations alone can now be used to construct a Fourier series for u ( r , ) which is convergent for any u Є U by virtue of condition 3 ° . Thus knowing the integrals along ellipses having eccentricity ranging in the interval arbitrarily ...
... relations alone can now be used to construct a Fourier series for u ( r , ) which is convergent for any u Є U by virtue of condition 3 ° . Thus knowing the integrals along ellipses having eccentricity ranging in the interval arbitrarily ...
Sayfa 31
... relation that the solution is bounded . Therefore , if we pass to the limit in ( 1 ) u1 ( M , M , t ) letting t → r ( M , M ) , the integral over DM , t will vanish . Moreover , O the ellipsoid of revolution degenerates to the line ...
... relation that the solution is bounded . Therefore , if we pass to the limit in ( 1 ) u1 ( M , M , t ) letting t → r ( M , M ) , the integral over DM , t will vanish . Moreover , O the ellipsoid of revolution degenerates to the line ...
Sayfa 46
... relations ( 5 ) v ( x , 0,1 ) = - √。= -x2th ( x , t ) at = h1 ( x , x ) , Let Kn - 2 ( x ) -2 The function v ( x ... relation ( 7 ) , we arrive at the integral equation λ ) G1 ( x , α ; 5,5 ) d§§n = g ( x , 1 ) , ( 8 ) D 8 ( x , 1 ) ...
... relations ( 5 ) v ( x , 0,1 ) = - √。= -x2th ( x , t ) at = h1 ( x , x ) , Let Kn - 2 ( x ) -2 The function v ( x ... relation ( 7 ) , we arrive at the integral equation λ ) G1 ( x , α ; 5,5 ) d§§n = g ( x , 1 ) , ( 8 ) D 8 ( x , 1 ) ...
İçindekiler
Generalization to Analytic Curves | 10 |
On the Problem of Determining a Function from Its Mean | 19 |
Two Formulations of the Linearized Inverse Problem | 28 |
Telif Hakkı | |
2 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 Akad belong boundary conditions CAUCHY data chapter coefficients consider const continuous function corresponding cosy Denote derive determining a function differential equation Dokl 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 HÖLDER condition hyperplane inequality 18 integral equation integral geometry integral-geometric problem Introduce the notation inverse kinematic inverse kinematic problem inversion formula kernel linearized inverse problem mean values multidimensional inverse problems Nauk SSSR obtain operator L defined parameters polar potential theory problem for equation problem of determining Problems for Differential R₁ R₂ right-hand side ROMANOV satisfies second kind solution to equation STURM-LIOUVILLE equations take FOURIER transforms telegraph equation travel-times two-parameter family unique solution uniqueness theorem unit circle values over spheres variables VOLTERRA equation waves wxxx