| Abstract: |
| In many evolution equations, solutions may become unbounded in finite
time. This phenomenon is often called blow-up and the finite time is called the blowup
time. To numerically reproduce the finite-time blow-up phenomenon, schemes
with adaptive time meshes were considered to be necessary. Since the numerical
blow-up time is defined by an infinite sum, which implies that one needs to compute
infinite times to achieve blow-up, this method cannot be carried out in real computation.
As a consequence, we revisit an algorithm accomplished by schemes with uniform time meshes for the computation of blow-up solutions. In this talk, we are concerned with a question: to what
extent can this algorithm be applied to compute the blow-up solutions and reproduce
the blow-up behavior? Our computational results for the semi-linear wave equation and the generalized Proudman-Johnson equation will be reported. |
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