Multidimensional Inverse Problems for Differential EquationsSpringer, 21 Ara 1970 - 59 sayfa |
Kitabın içinden
5 sonuçtan 1-3 arası sonuçlar
Sayfa 32
... Substituting this expression for a ( M ) in formula ( 8 ) of Sec . 1 , we arrive at the following nonlinear differential equation with shifted argument : 2 a u1 ( 4 ) = 2 su1 + at a [ r ( M , M ) u1 ( M , M , r ( M , M ) ) ] . ǝr ( MM ) ...
... Substituting this expression for a ( M ) in formula ( 8 ) of Sec . 1 , we arrive at the following nonlinear differential equation with shifted argument : 2 a u1 ( 4 ) = 2 su1 + at a [ r ( M , M ) u1 ( M , M , r ( M , M ) ) ] . ǝr ( MM ) ...
Sayfa 42
... Substituting the last inequality into ( 9 ) , we finally obtain ( 10 ) Introduce the notation | G ( w , λ ) | < απ 2,2 2 a - λ + w t = n - Ꭹ . p2 = a ( 10a ) 1 F1 ( w , t ) = F ( w2t + y 1 ) y1p Q1 ( w , p ) e = Q ( w , 11 √ 2 2 31 p ...
... Substituting the last inequality into ( 9 ) , we finally obtain ( 10 ) Introduce the notation | G ( w , λ ) | < απ 2,2 2 a - λ + w t = n - Ꭹ . p2 = a ( 10a ) 1 F1 ( w , t ) = F ( w2t + y 1 ) y1p Q1 ( w , p ) e = Q ( w , 11 √ 2 2 31 p ...
Sayfa 56
... Substituting ( 3 ) into ( 2 ) , we have ( 4 ) 21 00 b ( 5 , n , ) e -u - ivne -Wands = F2 ( u , v , w ) , F2 ( u , v , w ) = F1 [ w1 ( u , v , w ) , w2 ( u , v , w ) , wz ( u , v , w ) ] . Let ( 5 ) ∞ −1 ( u5 + vn ) .b ( 5 ̧n , 5 ) d5dn ...
... Substituting ( 3 ) into ( 2 ) , we have ( 4 ) 21 00 b ( 5 , n , ) e -u - ivne -Wands = F2 ( u , v , w ) , F2 ( u , v , w ) = F1 [ w1 ( u , v , w ) , w2 ( u , v , w ) , wz ( u , v , w ) ] . Let ( 5 ) ∞ −1 ( u5 + vn ) .b ( 5 ̧n , 5 ) d5dn ...
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