Computation of Morse decompositions for semilinear elliptic PDEs (Q2725058)
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scientific article; zbMATH DE number 1618701
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Computation of Morse decompositions for semilinear elliptic PDEs |
scientific article; zbMATH DE number 1618701 |
Statements
Computation of Morse decompositions for semilinear elliptic PDEs (English)
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15 July 2002
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semilinear elliptic problem
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bifurcation function
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Morse index
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Lyapunov-Schmidt reduction
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convergence
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numerical examples
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subdivision algorithm
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stability
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A numerical method for computing all solutions of a semilinear elliptic problem \(Au+g[u,\lambda]=0\) and their Morse indices is presented. The method uses an alternative problem analogous to the Lyapunov-Schmidt reduction and a corresponding finite dimensional analogue obtained via a finite element discretization. Convergence is analyzed. Several numerical examples are presented. For a fixed value of the bifurcation parameter \(\lambda\), a subdivision algorithm is used together with a priori estimates to find all solutions of a low dimensional bifurcation equation. The Morse indices of the computed solutions is then easily computed and stability of the solutions is determined.
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