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Elastic membrane equation in bounded and unbounded domains. (English) Zbl 1032.35039
The main purpose of this paper is to investigate local existence and uniqueness of solutions to the fourth-order evolutionary PDE describing transverse displacement of an extensible beam or membrane. The author furthermore derives several energy functionals nonincreasing along trajectories enabling thus to study long time behavior of solutions.

MSC:
35B40 Asymptotic behavior of solutions to PDEs
35B65 Smoothness and regularity of solutions to PDEs
74K10 Rods (beams, columns, shafts, arches, rings, etc.)
74K15 Membranes
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