We study the Cauchy problem of damped generalized Boussinesq equation utt - uxx ＋ （uxx＋ f（u））xx - αuxxt = 0. First we give the local existence of weak solution and smooth solution. Then by using potential well ...We study the Cauchy problem of damped generalized Boussinesq equation utt - uxx ＋ （uxx＋ f（u））xx - αuxxt = 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.展开更多
基金Supported by the National Natural Science Foundation of China(11471087,11101102)Ph.D.Programs Foundation of Ministry of Education of China(20102304120022)+3 种基金the Support Plan for the Young College Academic Backbone of Heilongjiang Province(1252G020)the Natural Science Foundation of Heilongjiang Province(A201014)Science and Technology Research Project of Department of Education of Heilongjiang Province(12521401)Foundational Science Foundation of Harbin Engineering University and Fundamental Research Funds for the Central Universities
文摘We study the Cauchy problem of damped generalized Boussinesq equation utt - uxx ＋ （uxx＋ f（u））xx - αuxxt = 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.
