Differential and Integral Equations

Global existence, uniqueness and regularity of solutions to a von Kármán system with nonlinear boundary dissipation

Angelo Favini, Mary Ann Horn, Irena Lasiecka, and Daniel Tataru

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Abstract

Systems of nonlinear elasticity described by Von Karman equations with nonlinear boundary dissipation are considered. Global existence, uniqueness of weakisolutions as well as the regularity of solutions with "smooth" data is established. Thus the paper solves, in particular, an outstanding problem of uniqueness of weak solutions to Von Karman system, which has been open in the literature even in the case of the homogeneous boundary data. This is accomplished by proving "sharp" regularity results of the Airy stress function.

Article information

Source
Differential Integral Equations, Volume 9, Number 2 (1996), 267-294.

Dates
First available in Project Euclid: 3 May 2013

Permanent link to this document
https://projecteuclid.org/euclid.die/1367603346

Mathematical Reviews number (MathSciNet)
MR1364048

Zentralblatt MATH identifier
0847.35070

Subjects
Primary: 35J65: Nonlinear boundary value problems for linear elliptic equations
Secondary: 35B65: Smoothness and regularity of solutions 35D05 73C50

Citation

Favini, Angelo; Horn, Mary Ann; Lasiecka, Irena; Tataru, Daniel. Global existence, uniqueness and regularity of solutions to a von Kármán system with nonlinear boundary dissipation. Differential Integral Equations 9 (1996), no. 2, 267--294. https://projecteuclid.org/euclid.die/1367603346


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See also

  • Related item: A. Favini, M. A. Horn, I. Lasiecka, D. Tataru. Addendum to the paper: "Global existence, uniqueness and regularity of solutions to a von Kármán system with nonlinear boundary dissipation". Differential and Integral Equations, Vol. 10, Iss. 1 (1997), 197-200.