Selection of steady states in the two-dimensional symmetric model of dendritic growth

Selection of steady needle crystals in the full nonlocal symmetric model of dendritic growth is considered. The diffusion equation and associated kinematic and thermodynamic boundary conditions are recast into a nonlinear integral equation which is solved numerically. For the range of P\'eclet numbers and capillarity lengths considered it is found that a smooth solution exists only if anisotropy is included in the capillarity term of the Gibbs-Thomson condition. The behavior of the selected velocity and tip radius as a function of undercooling is also examined.