The Hodograph Equation and \(\xi \) -Vector
摘要
The anisotropic hodograph equationEquationhodograph is derived and has a form of the acceleration and velocity dependent Herring-type equation. The hodograph equationEquationhodograph is the sharp-interfaceInterfacesharp limit of the diffuse interfaceInterfacediffuse model described by the phase field equation for slow and fast dynamics of the diffuse interfaceInterfacediffuse. The particular cases of the obtained hodograph equationEquationhodograph describe motion by mean interface curvatureInterfacecurvature, the relationship “velocity - Gibbs free energy”, and the Klein-Gordon and Born-Infeld equationsEquationBorn-Infeld related to the anisotropic propagation of various interfaces.