Differential and Integral Equations

Global solvability for damped abstract nonlinear hyperbolic systems

H. T. Banks, David S. Gilliam, and Victor I. Shubov

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We consider abstract nonlinear second-order-in-time systems with damping. The nonlinearity is assumed to satisfy a monotonicity condition as well as certain smoothness conditions. Well posedness of solutions is established and several examples of interest are discussed. A nonlinear variation-of-parameters representation for solutions in terms of an associated linear semigroup is also given.

Article information

Differential Integral Equations, Volume 10, Number 2 (1997), 309-332.

First available in Project Euclid: 2 May 2013

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 34G20: Nonlinear equations [See also 47Hxx, 47Jxx]
Secondary: 35L70: Nonlinear second-order hyperbolic equations 73G05 73K05


Banks, H. T.; Gilliam, David S.; Shubov, Victor I. Global solvability for damped abstract nonlinear hyperbolic systems. Differential Integral Equations 10 (1997), no. 2, 309--332. https://projecteuclid.org/euclid.die/1367526340

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