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Existence and uniqueness of solutions to a second order nonlinear nonlocal hyperbolic equation. (English) Zbl 1052.35137

Aizicovici, Sergiu (ed.) et al., Differential equations and control theory. Papers from the international workshop on differential equations and optimal control, Athens, OH, USA, May 12–14, 2000. New York, NY: Marcel Dekker (ISBN 0-8247-0681-1/pbk). Lect. Notes Pure Appl. Math. 225, 1-17 (2002).
Summary: We establish existence and uniqueness of weak solutions to a class of second order distributed parameter systems with sudden changes in the input term. Such systems are often encountered in flexible structures and structure-fluid interaction systems that utilize smart actuators. A Galerkin finite dimensional approximation scheme for computing the solution of these systems is developed and its strong convergence is proved. Numerical results are also presented.
For the entire collection see [Zbl 1044.35001].

MSC:

35L75 Higher-order nonlinear hyperbolic equations
35R10 Partial functional-differential equations
35L35 Initial-boundary value problems for higher-order hyperbolic equations
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
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