| Abstract: |
| We consider the blow-up problem of positive solutions to a quasilinear parabolic partial differential equation with zero Dirichlet boundary condition. This problem contains the case which is related to the curvature blow-up to the classical curvature flow. This case is a critical case, that is, it is well-known that the blow-up type is type II for this critical case and super critical case. And recently so-called loglog-type blow-up rate is proved for the critical case under very special conditions. So, there is a question: Is this loglog-type blow-up generic ? In this talk, we review the key observation for the critical case and show present mathematical results for super critical case (We haven`t get the estimates of the blow-up rate for this case.). Also we introduce a numerical method for estimating a blow-up rate by using scale invariance of the equation and show numerical observations for the critical and the super critical cases. |
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