Open Access. Powered by Scholars. Published by Universities.®
Articles 1 - 2 of 2
Full-Text Articles in Applied Mathematics
Infinitely Many Radially Symmetric Solutions To A Superlinear Dirichlet Problem In A Ball, Alfonso Castro, Alexandra Kurepa
Infinitely Many Radially Symmetric Solutions To A Superlinear Dirichlet Problem In A Ball, Alfonso Castro, Alexandra Kurepa
All HMC Faculty Publications and Research
In this paper we show that a radially symmetric superlinear Dirichlet problem in a ball has infinitely many solutions. This result is obtained even in cases of rapidly growing nonlinearities, that is, when the growth of the nonlinearity surpasses the critical exponent of the Sobolev embedding theorem. Our methods rely on the energy analysis and the phase-plane angle analysis of the solutions for the associated singular ordinary differential equation.
Wavenumber Selection Of Convection Rolls In A Box, Wayne Arter, Andrew J. Bernoff, A. C. Newell
Wavenumber Selection Of Convection Rolls In A Box, Wayne Arter, Andrew J. Bernoff, A. C. Newell
All HMC Faculty Publications and Research
The dynamics of two‐dimensional Rayleigh–Bénard convection rolls are studied in a finite layer with no‐slip, fixed temperature upper and lower boundaries and no‐slip insulating side walls. The dominant mechanism controlling the number of rolls seen in the layer is an instability concentrated near the side walls. This mechanism significantly narrows the band of stable wavenumbers although it can take a time comparable to the long (horizontal) diffusion time scale to operate.