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Zeitschrift für Analysis und ihre Anwendungen


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Volume 16, Issue 4, 1997, pp. 945–960
DOI: 10.4171/ZAA/798

Published online: 1997-12-31

A Nonlinear Beam Equation Arising in the Theory of Elastic Bodies

Karl Doppel[1], W. Herfort[2] and K. Pflüger[3]

(1) Freie Universität Berlin, Germany
(2) Freie Universität Berlin, Germany
(3) TU Wien, Austria

We study the global solvability of a nonlinear Cauchy problem, which arises in the theory of oscillations in elastic bodies. We show that the linearized problem defines a contraction semigroup, which is then used to transform the Cauchy problem into an integral equation. Finally, it is shown that the corresponding integral operator has a unique fixed point, which gives rise to a global solution of the original nonlinear problem.

Keywords: Nonlinear beam equations, global solvability, oscillations in elastic bodies, fixed point methods

Doppel Karl, Herfort W., Pflüger K.: A Nonlinear Beam Equation Arising in the Theory of Elastic Bodies. Z. Anal. Anwend. 16 (1997), 945-960. doi: 10.4171/ZAA/798