## Asymptotic and numerical analysis of linear and non-linear eigenvalue problems |

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### Contents

Nearly Circular Domains and Eigenvalue Asymptotics | 6 |

Domains Minimizing A2 for a Fixed i | 22 |

Criticality in a Nonlinear Eigenvalue Problem | 38 |

Copyright | |

3 other sections not shown

### Common terms and phrases

apply Green's theorem asymptotic expansions asymptotic results asymptotics and numerics behavior Bessel function boundary conditions Boundary perturbation calculated centered coefficients Aci Comparison of asymptotics computed consider constant cooling pellet cooling rod critical values curve defined denote derivatives determine differentiate Dirichlet boundary conditions Dirichlet Laplacian Doctor of Philosophy domain which minimizes eigenvalue pairs eigenvalue problem enddo equation expansions of Ac(e fixed full problem geometry given gradient Green's identity Green's theorem Henshaw and Keller higher eigenvalues inner product insulating rod integer laplacian logarithmic series minimizes A2 minimum multiplied nearly circular domain Neumann boundary conditions nodal line order correction perturbation theory PLTMG quantities radius Rayleigh quotient rod of circular Romberg integration second eigenfunction second eigenvalue second order shape solution solve spherical domain starting domain Substituting Table C.5 Temperature perturbation term expansion transitional parameters union of disks unit area unperturbed variable Vi(e Wed Aug 12 yields zero