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)

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

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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

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

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