## Communicated by G. F. Roach We consider the Cauchy problem for the damped Boussinesq equation governing long wave propagation in a viscous fluid of small depth. For the cases of one, two, and three space dimensions local in time existence and uniqueness of a solution is proved. We show that for
On global existence and uniqueness for the unilateral problem associated to the degenerated Kirchhoff equation
✍ Scribed by Cícero Lopes Frota; Nickolai A. Lar'kin
- Publisher
- Elsevier Science
- Year
- 1997
- Tongue
- English
- Weight
- 334 KB
- Volume
- 28
- Category
- Article
- ISSN
- 0362-546X
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The paper studies the existence and nonexistence of global solutions to the Cauchy problem for a nonlinear beam equation arising in the model in variational form for the neo-Hookean elastomer rod where k 1 ,k 2 > 0 are real numbers, g(s) is a given nonlinear function. When g(s) = s n (where n 2 is
## Abstract In this paper we prove the existence of global decaying __H__^2^ solutions to the Cauchy problem for a wave equation with a nonlinear dissipative term by constructing a stable set in __H__^1^(ℝ^__n__^ ). (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
A question of the existence of fiolutions of boundary-value problems for differential equations with parameter was considered by many authors, see [1]-[3] and [5]-[9]. The analogous problems for differential equations with a deviated argument was discussed in [8] and [3]. The purpose of this paper