Differential and Integral Equations

Global smooth solutions to a class of one-dimensional hyperbolic problems with boundary damping

Ph. Clément, Darmawijoyo, and W. T. van Horssen

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In this paper an initial--boundary-value problem for a nonlinear string (or wave) equation with nonclassical boundary conditions is considered. One end of the string is assumed to be fixed and the other end of the string is attached to a dashpot system, where the (positive) damping is generated. Existence, uniqueness, and regularity of solutions to this problem are investigated.

Article information

Differential Integral Equations, Volume 17, Number 1-2 (2004), 151-164.

First available in Project Euclid: 21 December 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35L70: Nonlinear second-order hyperbolic equations
Secondary: 35A05 35L20: Initial-boundary value problems for second-order hyperbolic equations 47H20: Semigroups of nonlinear operators [See also 37L05, 47J35, 54H15, 58D07]


Darmawijoyo; Clément, Ph.; van Horssen, W. T. Global smooth solutions to a class of one-dimensional hyperbolic problems with boundary damping. Differential Integral Equations 17 (2004), no. 1-2, 151--164. https://projecteuclid.org/euclid.die/1356060477

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