The Uniqueness of Certain Flows in a Channel With Arbitrary Cross Section
The Uniqueness of Certain Flows in a Channel With Arbitrary Cross Section
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In our eReader you can find the full English version of the book. Read The Uniqueness of Certain Flows in a Channel With Arbitrary Cross Section Online - link to read the book on full screen. Our eReader also allows you to upload and read Pdf, Txt, ePub and fb2 books. In the Mini eReder on the page below you can quickly view all pages of the book - Read Book The Uniqueness of Certain Flows in a Channel With Arbitrary Cross Section
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Besides this. It Is n ° n not difficult to verify that the eigenvalues A are either real or pure Imaginary numbers. It Is known that there can be only a finite number of eigenvalues In any bounded domain of the complex A-plane. It Is also well known that the above second order system defines a complete set of elgenfunctlons {^„(y)} such that a twice dlfferentlable function G(y) can be expanded In the Fourier series 00 G(y) = XZ "n^n^y) • n=0 13 It follows from the above remarks that for any fix...ed value of X, ')(l(x, y) has the unique expansion X (x, y) := ^^ = ZZ ^n^^)^n^y) > "1 1 Y 1 • o^*^ "^ n=0 Here, the coefficient ct^fx) is a^{x) =J PQ(y)u^{y)X(x, y)^n^y^^y -1 and as a function of x it must satisfy dx _-, V- = j po^o^xx^y = -/ [|rPo-oXy-Poy^l^n^y -1 = - ^n / Po^o-X V^ • -1 Hence the coefficient a^(x) must satisfy ^ — + -K'^a (x = , 2 n n^ ^ dx from which a^(x) = a^ cos A^x + b^ sin A^(x), \ ^ ^ (3. 15) Ik This shows that if 'X (x, y) Is to be bounded everywhere then If a.
What to read after The Uniqueness of Certain Flows in a Channel With Arbitrary Cross Section?
You can find similar books in the "Read Also" column, or choose other free books by Arthur S Peters to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
Besides this. It Is n ° n not difficult to verify that the eigenvalues A are either real or pure Imaginary numbers. It Is known that there can be only a finite number of eigenvalues In any bounded domain of the complex A-plane. It Is also well known that the above second order system defines a complete set of elgenfunctlons {^„(y)} such that a twice dlfferentlable function G(y) can be expanded In the Fourier series 00 G(y) = XZ "n^n^y) • n=0 13 It follows from the above remarks that for any fix...ed value of X, ')(l(x, y) has the unique expansion X (x, y) := ^^ = ZZ ^n^^)^n^y) > "1 1 Y 1 • o^*^ "^ n=0 Here, the coefficient ct^fx) is a^{x) =J PQ(y)u^{y)X(x, y)^n^y^^y -1 and as a function of x it must satisfy dx _-, V- = j po^o^xx^y = -/ [|rPo-oXy-Poy^l^n^y -1 = - ^n / Po^o-X V^ • -1 Hence the coefficient a^(x) must satisfy ^ — + -K'^a (x = , 2 n n^ ^ dx from which a^(x) = a^ cos A^x + b^ sin A^(x), \ ^ ^ (3. 15) Ik This shows that if 'X (x, y) Is to be bounded everywhere then If a.
What to read after The Uniqueness of Certain Flows in a Channel With Arbitrary Cross Section?
You can find similar books in the "Read Also" column, or choose other free books by Arthur S Peters to read onlineMoreLess
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