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A bundle view of boundary-value problems: generalizing the Gardner–Jones bundle by Francis R. Austin; Thomas J. Bridges is a Mathematics article available to read on EtoBox.
What is A bundle view of boundary-value problems: generalizing the Gardner–Jones bundle about?
Holomorphic families of linear ordinary differential equations on a finite interval with prescribed parameter-dependent boundary conditions are considered from a geometrical viewpoint. The Gardner-Jones bundle, which was introduced for linearized reaction-diffusion equations, is generalized and applied to this abstract class of l-dependent boundary-value problems, where l is a complex eigenvalue parameter. The fundamental analytical object of such boundary-value problems (BVPs) is the characteristic determinant, and it is proved that any characteristic determinant on a Jordan curve can be characterized geometrically as the determinant of a transition function associated with the Gardner-Jones bundle. The topology of the bundle, represented by the Chern number, then yields precise information about the number of eigenvalues in a prescribed subset of the complex l-plane. This result shows that the Gardner-Jones bundle is an intrinsic geometric property of such l-dependent BVPs. The bundle framework is applied to examples from hydrodynamic stability theory and the linearized complex Ginzburg-Landau equation.
Who reads A bundle view of boundary-value problems: generalizing the Gardner–Jones bundle?
It is typically read by researchers, students, and practitioners in Mathematics.
- Author
- Francis R. Austin; Thomas J. Bridges
- Publisher
- Elsevier Science; Elsevier ; Elsevier Inc.; Elsevier BV (ISSN 0022-0396)
- Published
- 2003
- Language
- EN
- Field
- Mathematics (Physical Sciences)