Blowup of solutions for the “bad” Boussinesq-type equation

The paper studies the blowup of solutions to the initial boundary value problem for the “bad” Boussinesq-type equation <f>utt−uxx−buxxxx=σ(u)xx</f>, where <f>b>0</f> is a real number and <f>σ(s)</f> is a given nonlinear function. By virtue of the energy method and the Fourier transform method, respectively, it proves that under certain assumptions on <f>σ(s)</f> and initial data, the generalized solutions of the above-mentioned problem blow up in finite time. And a few examples are shown, especially for the “bad” Boussinesq equation, two examples of blowup of solutions are obtained numerically. [Copyright &y& Elsevier]