一类非线性发展方程整体解的存在性、渐近性与解的爆破

研究一类非线性发展方程初边值问题整体弱解的存在性，渐近性和解的爆破问题，证明在关于非线性项的不同条件下，上述初边值问题分别在大初值和小初始能量的情况下存在整体弱解，并且讨论了弱解的渐近性。还证明：在相反的条件下，上述弱解在有限时刻爆破，并且给出了一个实例。

Global Existence, Asymptotic Behavior and Blowup of Solutions to a Nonlinear Evolution Equation

The paper studies the global existence, asymptotic behavior and blowup of weak solutions to the initial bounary value problem of a nonlinear evolution equation. It proves that under certain different assumptions on nonlinear terms, the above-mentioned problem admits a global weak solution for large initial data and small initial energy, respectively, and the asymptotic behavior of the solution is also discussed. It also proves that under the opposite assumptions the weak solutions blow up in finite time. And an example is shown.