Über das homogene Dirichlet-Problem bei nichtlinearen partiellen Differentialgleichungen vom Typ der Boussinesq-Gleichung
In: Mathematical Methods in the Applied Sciences, Jg. 9 (1987), S. 493-519
Online
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Zugriff:
Semilinear equations of Boussinesq type, e.g. utt + uxx − uxxxx + (u2)xx = 0, utt + uxx − uxxxx + uxuxx = 0, or certain equations containing the squared wave operator, e.g. uxxtt − uk = 0, k ϵ Nk ≥ 2, are studied. A generalized boundary value problem on bounded domains can be treated using Hilbert space methods. The linear parts of these equations are not elliptic, the latter not even hypoelliptic. A mountain pass lemma is used to prove the existence of nontrivial weak solutions. These solutions are obtained in anisotropic Sobolev spaces.
Titel: |
Über das homogene Dirichlet-Problem bei nichtlinearen partiellen Differentialgleichungen vom Typ der Boussinesq-Gleichung
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Autor/in / Beteiligte Person: | Hsiao, G. C. ; Warnecke, Gerald |
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Zeitschrift: | Mathematical Methods in the Applied Sciences, Jg. 9 (1987), S. 493-519 |
Veröffentlichung: | Wiley, 1987 |
Medientyp: | unknown |
ISSN: | 0170-4214 (print) |
DOI: | 10.1002/mma.1670090133 |
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