Multidimensional Inverse Problems for Differential EquationsSpringer, 15 Kas 2006 - 58 sayfa |
Kitabın içinden
17 sonuçtan 1-5 arası sonuçlar
Sayfa 1
... defined in a domain through its integrals along a family of curves in the domain . One of the earliest and most familiar versions of such problems is the determination of a continuous function of n - variables through its mean values ...
... defined in a domain through its integrals along a family of curves in the domain . One of the earliest and most familiar versions of such problems is the determination of a continuous function of n - variables through its mean values ...
Sayfa 2
... defined by O ( 1 ) r ( x , s , 0,0 ) + r ( x , s , x ° , 0 ) = t where r ( x , s , 0,0 ) and the foci ( 0,0 ) and r ( x , s , x ° , 0 ) are the distances between ( x , s ) and ( x ° , 0 ) , respectively . Thus , let the function v ( x ...
... defined by O ( 1 ) r ( x , s , 0,0 ) + r ( x , s , x ° , 0 ) = t where r ( x , s , 0,0 ) and the foci ( 0,0 ) and r ( x , s , x ° , 0 ) are the distances between ( x , s ) and ( x ° , 0 ) , respectively . Thus , let the function v ( x ...
Sayfa 3
... ) . - ( 5 ) u ( r cos , r sin ) d = v ( p , e ) v ( p , c ) , > with r given by ( 4 ) . We apply to both sides of ( 5 ) the operator L defined by ( 6 ) Lv = p P 9/5 де S v ( z , e ) dz Z > When equation ( 5 ) has a solution in - 3 -
... ) . - ( 5 ) u ( r cos , r sin ) d = v ( p , e ) v ( p , c ) , > with r given by ( 4 ) . We apply to both sides of ( 5 ) the operator L defined by ( 6 ) Lv = p P 9/5 де S v ( z , e ) dz Z > When equation ( 5 ) has a solution in - 3 -
Sayfa 4
... define ( k = 1,2,3 , ... ) L ° v = v ( p , c ) , formula ( 8 ) is also valid for k = 0. Thus we have constructed in unique fashion a system of moments on each ellipse . Since u ( x , s ) is an even function of s , it is uniquely de ...
... define ( k = 1,2,3 , ... ) L ° v = v ( p , c ) , formula ( 8 ) is also valid for k = 0. Thus we have constructed in unique fashion a system of moments on each ellipse . Since u ( x , s ) is an even function of s , it is uniquely de ...
Sayfa 6
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İçindekiler
1 | |
Linearized Inverse Dynamic Problem for the Telegraph | 22 |
Derivation of a Nonlinear Differential Equation for | 31 |
CHAPTER 4 | 39 |
CHAPTER 5 | 52 |
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 belong boundary conditions CAUCHY data chapter consider const construct 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 f(x,y functions u(r fundamental solution given GREEN'S function half-plane half-space HÖLDER condition hyperplane inequality 16 initial and boundary integral equation integral geometry integral-geometric problem Introduce the notation Inverse Kinematic Inverse Kinematic Problem inversion formula kernel L₁(D linearized inverse problem M₁ mean values multidimensional inverse problems obtain operator L defined parameters polar problem for equation problem of determining Q₂ R₂ relations right-hand side second kind sense of HADAMARD SM,t solution to equation space STURM-LIOUVILLE equations 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 ду