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Eigenvalue estimates and existence for a generalised Graetz problem
Journal article   Open access   Peer reviewed

Eigenvalue estimates and existence for a generalised Graetz problem

A.S Jones, D.E Stewart and H.B Thompson
Journal of mathematical analysis and applications, Vol.141(1), pp.152-163
1989
DOI: 10.1016/0022-247X(89)90212-6
url
https://doi.org/10.1016/0022-247X(89)90212-6View
Published (Version of record) Open Access

Abstract

The study of forced convection of heat through tubes leads to the study of eigenvalue problems for the Laplacian in which the eigenvalue appears quadratically. Estimates for the eigenvalues based on the eigenvalues of the Laplacian operator are derived. From these estimates the existence of a countable set of eigenvalues is derived. Furthermore, counting multiplicities, the set of eigenvalues can be put in one-to-one correspondence with the eigenvalues of the Laplacian. These results are then generalised to cover a class of selfadjoint linear elliptic partial differential equations in which the eigenvalue appears non-linearly.

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