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
在这份报纸，我们为一般非线性的过滤方程 ut-Dj 考虑 nonnegative 答案到 Cauchy 问题( aij ( x ， t ， u ) Di (u)) +bi ( t ， u ) Diu+C ( x ， t ， u ) =0 ，并且获得存在，在在一些结构条件下面的这些答案的有限时间的唯一和发作。
Lipschitz continuous solutions to the Cauchy problem for 1-D first order quasi-linear hyperbolic systems are considered. Based on the methods of approximation and integral equations, the author gives two definitions o...Lipschitz continuous solutions to the Cauchy problem for 1-D first order quasi-linear hyperbolic systems are considered. Based on the methods of approximation and integral equations, the author gives two definitions of Lipschitz solutions to the Cauchy problem and proves the existence and uniqueness of solutions.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Foundation item： Supported by National Science Foundation of China（10572156） Supported by Natural Science Foundation of Henan Province（0211010900） Supported by National Science Foundation of Department of Education of Henan Province（200510465001）
文摘在这份报纸，我们为一般非线性的过滤方程 ut-Dj 考虑 nonnegative 答案到 Cauchy 问题( aij ( x ， t ， u ) Di (u)) +bi ( t ， u ) Diu+C ( x ， t ， u ) =0 ，并且获得存在，在在一些结构条件下面的这些答案的有限时间的唯一和发作。
文摘Lipschitz continuous solutions to the Cauchy problem for 1-D first order quasi-linear hyperbolic systems are considered. Based on the methods of approximation and integral equations, the author gives two definitions of Lipschitz solutions to the Cauchy problem and proves the existence and uniqueness of solutions.
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.
