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Compensated compactness and time-periodic solutions to non-autonomous quasilinear telegraph equations. (English) Zbl 0737.35040

Author’s summary: In the present paper, the existence of a weak time- periodic solution to the nonlinear telegraph equation \(U_{tt}+dU_ t- \sigma(x,t,U_ x)_ x+aU=f(x,t,U_ x,U_ t,U)\) with Dirichlet boundary conditions is proved. No “smallness” assumptions are made concerning the function \(f\). The main idea of the proof relies on the compensated compactness theory.
Reviewer: D.Huet (Nancy)

MSC:

35L70 Second-order nonlinear hyperbolic equations
35D05 Existence of generalized solutions of PDE (MSC2000)
47J25 Iterative procedures involving nonlinear operators
35B10 Periodic solutions to PDEs
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