In this paper, we consider the blow-up solutions for a quasilinear parabolic partial differential equation . We numerically investigate the blow-up rates of these solutions by using a numerical method which is recently proposed by the authors [3].
Modern physics theories claim that the dynamics of interfaces between the two-phase is described by the evolution equations involving the curvature and various kinematic energies. We consider the motion of spiral-shaped polygonal curves by its crystalline curvature, which deserves a mathematical model of real crystals. Exploiting the comparison principle, we show the local existence and uniqueness of the solution.
Page 1