| Abstract: |
| Many nonlinear evolution equations possess solutions which blow up in finite time. It is one of the most interesting issues concerning blow-up phenomena how the solutions develop singularities.
To determine the blow-up rate is a major problem in such a direction.
Depending on the equations, blow-up rates take the forms of various types such as simple power type and logarithmic type, and even more complex ones.
There are vast amounts of literature deeply considering how solutions blow up. To our best knowledge, however, only a few studies have investigated numerical methods for blow-up rates.
In this talk, we propose a simple but effective numerical method which estimates blow-up rates for a class of nonlinear evolution equations. Here, we consider the class of equations which satisfy a scaling invariance. Thanks to this scaling invariance, we adopt the rescaling algorithm and construct a sequence whose behavior leads to the blow-up rate. Applying the method to several nonlinear equations, we examine the effectiveness of the method. We show that our method is applicable to not only the simple power type blow-up rates but also more complex ones. |
|