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Mathematische Methoden I / Mathematical Methods I

Mathematische Methoden I / Mathematical Methods I


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Ziff. 57. 313 ist. Die letzten beiden Gleichungen geIten aber nicht mehr fUr eine Losung (56.5), bei der sowohl w wie auch a willkiirlich vorgegeben sind. Dies ware ja auch im Widerspruch zu dem in Ziff. 47 fUr die Potentialgleichung bewiesenen Satz, daB nicht gleichzeitig beide Randwerte "P und o"P/on willkiirlich vorgegeben werden konnen. Wenn w und a willkiirlich vorgegeben sind, stellt (56.5) zwar im Innern auch eine Losung der Differentialgleichung (56.2) dar, fUr die aber bei Annaherung an den Rand die Werte "P und o"P/on nicht gegen - 4na bzw. 4nw konvergieren. Gl. (56.4) zeigt, wie auch bei unstetigen Randbedingungen "P (r) im Innern des Gebietes samt den auftretenden Ableitungen stetig wird, sofern nur e (r) selbst diese Eigenschaften hat. Diese Tatsache, die schon fUr die zweidimensionale Potentialgleichung aus der Funktionentheorie entnommen wurde, zeigt wieder einen deutlichen Unterschied der elliptischen Differentialgleichung (56.2) gegen- iiber der hyperbolischen Wellengleichung. Bei der Wellengleichung pflanzt sich eine Unstetigkeit der Anfangswerte durch das raum-zeitliche Grundgebiet langs der Charakteristiken fort. Hier dagegen gibt es keine reellen Charakteristiken, und Unstetigkeiten der Randwerte setzen sich nicht in das Grundgebiet fort. III. Eigenwertprobleme. 57. Problemstellung. Es solI vorausgesetzt werden, daB die lineare Differential- gleichung zweiter Ordnung (57.1 ) als passenden Rand einen geschlossenen Rand zulaBt, der als Oberflache ein "Grundgebiet" abgrenzt. Es solI also ein "echtes" Randwertproblem vorliegen.


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Product Details
  • ISBN-13: 9783642458347
  • Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
  • Binding: Paperback
  • Height: 244 mm
  • No of Pages: 364
  • Series Title: German
  • Weight: 648 gr
  • ISBN-10: 3642458343
  • Publisher Date: 03 Oct 2013
  • Edition: Softcover Reprint of the Origi ed.
  • Language: German
  • Returnable: Y
  • Spine Width: 20 mm
  • Width: 170 mm


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Mathematische Methoden I / Mathematical Methods I
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