Classification of Radial Solutions Arising in the Study of Thermal Structures with Thermal Equilibrium or no Flux at the Boundary

Title

Classification of Radial Solutions Arising in the Study of Thermal Structures with Thermal Equilibrium or no Flux at the Boundary

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Description

We provide a complete classification of the radial solutions to a class of reaction diffusion equations arising in the study of thermal structures such as plasmas with thermal equilibrium or no flux at the boundary. In particular, our study includes rapidly growing nonlinearities, that is, those where an exponent exceeds the critical exponent. We describe the corresponding bifurcation diagrams and determine existence and uniqueness of ground states, which play a central role in characterizing those diagrams. We also provide information on the stability-unstability of the radial steady states.

ISBN

9780821847268

Publication Date

4-2010

Publisher

American Mathematical Society

City

Providence, RI

Keywords

Radial solution, unstable solution, stable solution, thermal structure, free boundary problem, ground states, equilibrium temperature

Disciplines

Applied Mathematics | Ordinary Differential Equations and Applied Dynamics | Partial Differential Equations | Physical Sciences and Mathematics

Comments

This is number 976 in the series Memoirs of the American Mathematical Society.

Also available as an ebook at http://www.ams.org/books/memo/0976/.