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

✍ Scribed by Zhijian Yang; Xia Wang

Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
169 KB
Volume
285
Category
Article
ISSN
0022-247X

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✦ Synopsis

The paper studies the blowup of solutions to the initial boundary value problem for the "bad" Boussinesq-type equation u ttu xxbu xxxx = σ (u) xx , where b > 0 is a real number and σ (s) is a given nonlinear function. By virtue of the energy method and the Fourier transform method, respectively, it proves that under certain assumptions on σ (s) 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.

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