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- W2460205076 abstract "Nonlinear eigenvalue problems are considered for partial differential equations and boundary conditions of the for The problems are perturbed by deleting a small subdomain Dε from D and imposing a boundary condition on the surface of the resulting hole, or else by changing the constant b in the boundary condition to a different constant ε−1k on a small part of ∂D. In both cases the perturbed solution is constructed for ε small by the method of matched asymptotic expansions. Particular attention is paid to the calculation of λc(ε), the critical value of λ at which the number of solutions changes by two, for example from two to none. This value of λ represents a simple fold point in the bifurcation diagram of ‖u‖ versus λ. The analysis is applied to chemical reactors with F(x,u)=eu, in which case λc is the critical value of the Frank-Kamenetskii parameter. The asymptotic results are compared with exact and numerical results for some special cases, and fair agreement is found. Some previous asymptotic calculations are found to be incorrect." @default.
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- W2460205076 date "1991-07-01" @default.
- W2460205076 modified "2023-09-26" @default.
- W2460205076 title "Nonlinear Eigenvalue Problems under Strong Localized Perturbations with Applications to Chemical Reactors" @default.
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- W2460205076 doi "https://doi.org/10.1002/sapm19918511" @default.
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