一类非线性抛物方程组解的性质(英文)

Property of the solutions of a class of nonlinear parabolic systems

考虑具非局部弱耦合源的一类非线性退化抛物方程组的Dirichlet初边值问题。由于方程的退化性,主要考虑弱解的性质。利用已有结论该系统存在唯一弱解并满足比较原理。利用上下解方法,证明当空间区域包含一个充分大的球时,该初边值问题的解在有限时刻爆破。

The Dirichlet initial boundary problem of a nonlinear degenerate parabolic system with non-local coupled weak sources is considered. Due to the degeneracy of the system, main effort is focused on the discussion of the properties of weak solutions. With previous results, the existence and uniqueness of weak solutions has been established, and the weak solutions satisfy the comparison principle. By the method of supersolution and subsolution, it is shown that the solution will blow up in finite time if the domain contains a sufficiently large ball.