Global existence and blow up for damped generalized Boussinesq equation
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We study the Cauchy problem of damped generalized Boussinesq equation u tt − u xx + (u xx + f(u)) xx − αu xxt = 0. First we give the local existence of weak solution and smooth solution. Then by using potential well method and convexity method we prove the global existence and finite time blow up of solution, then we obtain some sharp conditions for the well-posedness problem.
Keywordsgeneralized Boussinesq equation damping Cauchy problem global existence blow up
2000 MR Subject Classification35Q35
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We do appreciate the referee’s so many valuable suggestions, which corrected some mistakes in the paper and improved the paper a lot.
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