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Über das homogene Dirichlet-Problem bei nichtlinearen partiellen Differentialgleichungen vom Typ der Boussinesq-Gleichung (1987)

Warnecke, G. ; Hsiao, G. C.

Chichester, West Sussex : Wiley-Blackwell

Mathematical Methods in the Applied Sciences 9 (1987), S. 493-519

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ISSN: 0170-4214

Keywords: Mathematics and Statistics ; Applied Mathematics

Source: Wiley InterScience Backfile Collection 1832-2000

Topics: Mathematics

Notes: 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 ∊ N k ≥ 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.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1002/mma.1670090133

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