Classification of Radial Solutions Arising in the Study of Thermal Structures with Thermal Equilibrium or no Flux at the Boundary
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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.
American Mathematical Society
Radial solution, unstable solution, stable solution, thermal structure, free boundary problem, ground states, equilibrium temperature
Applied Mathematics | Ordinary Differential Equations and Applied Dynamics | Partial Differential Equations | Physical Sciences and Mathematics
Castro, Alfonso and Padrón, Victor, "Classification of Radial Solutions Arising in the Study of Thermal Structures with Thermal Equilibrium or no Flux at the Boundary" (2010). All HMC Faculty Books. 8.