Mathematical point of view for degenerate scale (Laplace and Navier equations)

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# Mathematical point of view for degenerate scale (Laplace and Navier equations) - PowerPoint PPT Presentation

Mathematical point of view for degenerate scale (Laplace and Navier equations). Feng Kang ( 馮康院士 ) BIE and PDE are not equivalent Hu Hachang ( 胡海昌院士 ) ( 錢令希院士 ) The solution of PDE satisfies the BIE ? The solution of BIE satisfies the PDE ?

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Mathematical point of view for degenerate scale (Laplace and Navier equations)

Feng Kang (馮康院士)

BIE and PDE are not equivalent

Hu Hachang (胡海昌院士) (錢令希院士)

The solution of PDE satisfies the BIE ?

The solution of BIE satisfies the PDE ?

A necessary and sufficient BIE formulation ?

1

Operator

Range base

Domain base

Mathematical point of view for degenerate scale (vector and function spaces)

Fredholm alternative theorem

SVD

x: any vector

infinite solution

no solution

Rank deficient matrix

Vector space

Fredholm alternative theorem

Not sufficient: add constraint

infinite solution

Not necessary

no solution

Mathematical point of view for degenerate scale (vector and function spaces)

Operator

Range base

Domain base

Function space

Weakly singular kernel

SVE

Fredholm alternative theorem

Not sufficient: add constraint

infinite solution: b no \phi_3

3

no solution: b there is \phi_3

Not necessary