Eigenvalue estimates and existence for a generalised Graetz problem

Jones A.S., Stewart D.E. and Thompson H.B. (1989) Eigenvalue estimates and existence for a generalised Graetz problem. Journal of Mathematical Analysis and Applications, 141 1: 152-163. doi:10.1016/0022-247X(89)90212-6


Author Jones A.S.
Stewart D.E.
Thompson H.B.
Title Eigenvalue estimates and existence for a generalised Graetz problem
Journal name Journal of Mathematical Analysis and Applications
ISSN 1096-0813
Publication date 1989-01-01
Sub-type Article (original research)
DOI 10.1016/0022-247X(89)90212-6
Open Access Status Not yet assessed
Volume 141
Issue 1
Start page 152
End page 163
Total pages 12
Subject 2603 Analysis
2604 Applied Mathematics
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.
Q-Index Code C1
Q-Index Status Provisional Code
Institutional Status Unknown

Document type: Journal Article
Sub-type: Article (original research)
Collection: Scopus Import - Archived
 
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