On the asymptotic behavior of solutions of inhomogeneous second-order quasilinear partial differential equations

Horgan, C. O.; Payne, L. E.

doi:10.1090/qam/1031690

Authors: C. O. Horgan and L. E. Payne
Journal: Quart. Appl. Math. 47 (1989), 753-771
MSC: Primary 35B40; Secondary 35J65, 73B99, 73C50
DOI: https://doi.org/10.1090/qam/1031690
MathSciNet review: MR1031690
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Abstract: This paper is concerned with the asymptotic behavior of solutions of a class of inhomogeneous second-order quasilinear partial differential equations in two independent variables defined over rectangular plane domains whose lengths greatly exceed their widths. Solutions to a Dirichlet problem for such equations are shown to be well approximated, away from the ends of the rectangle, by solutions to the corresponding one-dimensional problem for an ordinary differential equation on the cross-section of the rectangle. Applications to problems in geometry and nonlinear continuum mechanics are discussed.

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