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Classification of Radial Solutions Arising in the Study of Thermal Structures with Thermal Equilibrium or No Flux at the Boundary
Alfonso Castro, Harvey Mudd College, Claremont, CA, and Víctor Padrón, Normandale Community College, Bloomington, MN

Memoirs of the American Mathematical Society
2010; 72 pp; softcover
Volume: 208
ISBN-10: 0-8218-4726-0
ISBN-13: 978-0-8218-4726-8
List Price: US$68
Individual Members: US$40.80
Institutional Members: US$54.40
Order Code: MEMO/208/976
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The authors 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, their study includes rapidly growing nonlinearities, that is, those where an exponent exceeds the critical exponent. They describe the corresponding bifurcation diagrams and determine existence and uniqueness of ground states, which play a central role in characterizing those diagrams. They also provide information on the stability-unstability of the radial steady states.

Table of Contents

  • Introduction
  • Bifurcation diagrams
  • Oscillation properties
  • Ground states
  • Stability of thermal structures
  • Proof of main theorems
  • The degenerate case, \(k=-1\)
  • Appendix 1. The conservative case \((N=1)\)
  • Appendix 2. Pohozaev identity
  • Bibliography
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