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Compensated compactness and time-periodic solutions to non-autonomous quasilinear telegraph equations

Eduard Feireisl (1990)

Aplikace matematiky

In the present paper, the existence of a weak time-periodic solution to the nonlinear telegraph equation U t t + d U t - σ ( x , t , U x ) x + a U = f ( x , t , U x , U t , U ) with the 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.

Continuation of invariant subspaces via the Recursive Projection Method

Vladimír Janovský, O. Liberda (2003)

Applications of Mathematics

The Recursive Projection Method is a technique for continuation of both the steady states and the dominant invariant subspaces. In this paper a modified version of the RPM called projected RPM is proposed. The modification underlines the stabilization effect. In order to improve the poor update of the unstable invariant subspace we have applied subspace iterations preconditioned by Cayley transform. A statement concerning the local convergence of the resulting method is proved. Results of numerical...

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