Analytical Solution of Governing Equations for Three-dimension Steady State Crystal Growth

A class of partial differential equations (PDE) which describe three-dimension steady state crystal growth for concentration were studied. Because there exists far-field condition, their exact solution or numerical solution can not be derived based on known results about PDE. By using variables separation in the complex number field, the real analytical solution in the form of Fourier series was obtained. The result shows that the concentration in the solid-liquid interface is exponentially damped oscillation.