Stability of the Faedo-Galerkin approximation of nonlinear wave-equations |
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Authors: | Klaus -Günther Strack |
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Affiliation: | 1. Institut für Geometrie und Praktische Mathematik der RWTH Aachen, Deutschland
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Abstract: | Present investigation analyses the Ljapunov stability of the systems of ordinary differential equations arising in then-th step of the Faedo-Galerkin approximation for the nonlinear wave-equation $$\begin{gathered} u_{tt} - u_{xx} + M(u) = 0 \hfill \\ u(0,t) = u(1,t) = 0 \hfill \\ u(x,0) = \Phi (x); u_t (x,0) = \Psi (x). \hfill \\ \end{gathered}$$ For the nonlinearities of the classM (u)=u 2 p+1 ,p ∈N, ann-independent stability result is given. Thus also the stability of the original equation is shown. |
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