A Nonlinear Beam Equation Arising in the Theory of Elastic Bodies
Karl Doppel
Freie Universität Berlin, GermanyW. Herfort
Freie Universität Berlin, GermanyK. Pflüger
TU Wien, Austria
![A Nonlinear Beam Equation Arising in the Theory of Elastic Bodies cover](/_next/image?url=https%3A%2F%2Fcontent.ems.press%2Fassets%2Fpublic%2Fimages%2Fserial-issues%2Fcover-zaa-volume-16-issue-4.png&w=3840&q=90)
Abstract
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.
Cite this article
Karl Doppel, W. Herfort, K. Pflüger, A Nonlinear Beam Equation Arising in the Theory of Elastic Bodies. Z. Anal. Anwend. 16 (1997), no. 4, pp. 945–960
DOI 10.4171/ZAA/798