In this article, the existence, uniqueness and regularities of the global generalized solution and global classical solution for the periodic boundary value problem and the Cauchy problem of the general cubic double d...In this article, the existence, uniqueness and regularities of the global generalized solution and global classical solution for the periodic boundary value problem and the Cauchy problem of the general cubic double dispersion equationutt - uxx - auxxtt ＋ bux4 - duxxt = f（u）xxare proved, and the sufficient conditions of blow-up of the solutions for the Cauchy problems in finite time are given.展开更多
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
This paper is concerned with the global existence and pointwise estimates of solutions to the generalized Benjamin-Bona-Mahony equations in all space dimensions.By using the energy method, Fourier analysis and pseudo-...This paper is concerned with the global existence and pointwise estimates of solutions to the generalized Benjamin-Bona-Mahony equations in all space dimensions.By using the energy method, Fourier analysis and pseudo-differential operators, the global existence and pointwise convergence rates of the solution are obtained. The decay rate is the same as that of the heat equation and one can see that the solution propagates along the characteristic line.展开更多
In this paper the authors give a complete result on the global existence andthe lifesspan of classical solutions to the Cauchy problem for a kind 0f quasilillear partialdifferelitial equations of physical interest. Th...In this paper the authors give a complete result on the global existence andthe lifesspan of classical solutions to the Cauchy problem for a kind 0f quasilillear partialdifferelitial equations of physical interest. The equation concerned is a quasiIinear hyper-bolic equation with higher order dissipative term. The meth0d presented here offers an approach which can be used to look for some explicit exact solutions of physical interest.展开更多
文摘In this article, the existence, uniqueness and regularities of the global generalized solution and global classical solution for the periodic boundary value problem and the Cauchy problem of the general cubic double dispersion equationutt - uxx - auxxtt ＋ bux4 - duxxt = f（u）xxare proved, and the sufficient conditions of blow-up of the solutions for the Cauchy problems in finite time are given.
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.
基金supported by the National Natural Science Foundation of China(No.11101121)
文摘This paper is concerned with the global existence and pointwise estimates of solutions to the generalized Benjamin-Bona-Mahony equations in all space dimensions.By using the energy method, Fourier analysis and pseudo-differential operators, the global existence and pointwise convergence rates of the solution are obtained. The decay rate is the same as that of the heat equation and one can see that the solution propagates along the characteristic line.
基金The authors would like to thank the referees for the careful reading of this paper and for the valuable suggestions to improve the presentation and the style of the paper. This project is supported by Key Scientific Research Foundation of the Higher Education Institutions of Henan Province, China （No. 15A110017） and National Natural Science Foundation of China （No. 11526077）.
文摘In this paper the authors give a complete result on the global existence andthe lifesspan of classical solutions to the Cauchy problem for a kind 0f quasilillear partialdifferelitial equations of physical interest. The equation concerned is a quasiIinear hyper-bolic equation with higher order dissipative term. The meth0d presented here offers an approach which can be used to look for some explicit exact solutions of physical interest.
