Robin边界条件下更一般化的非线性抛物问题全局解的存在性和爆破

Blow-up and Global Existence of the Solution to Some More General Nonlinear Parabolic Problems with Robin Boundary Conditions

本文主要研究了Robin边界条件下更一般化的非线性抛物问题解的爆破现象以及全局解的存在性．通过对问题中的已知函数进行适当的假设，建立适当的辅助函数，应用微分不等式技术，当问题的解发生爆破时得到了解的爆破时间的下界．这种类型的下界在物理学、生物学、天文学等领域有着广泛的应用．同时，也推导了问题的解全局存在的条件．

In this paper, we consider the blow-up phenomena and global existence of the solution to a more general nonlinear parabolic problem under Robin boundary condition. By giving some suitable restrictive conditions on the known functions and applying a differential inequality technique, a lower bound for blow-up time of solution is derived when the blow-up occurs. This type of lower bound is widely used in physics, biology, astronomy and other many fields. The global existence of the solution is also proved.