一类具有外部扩散及非线性边界流问题解的爆破
A Class of Blow-Up Solution with External Diffusion and Nonlinear Boundary Flow Problems
摘要:
本文研究了一类具有外部扩散及非线性边界流问题，利用构造辅助函数，结合极值原理，利用经典的微分不等式，分别得到了其在Neumman边界和Dirichlet边界下爆破解存在的充分条件，爆破时刻的上界估计，最后给出了定理在两个非线性问题中的具体应用。
Abstract:
In this paper, we study a class of problems with external diffusion and nonlinear boundary flow. By using the construction auxiliary function and the maximum principle, the sufficient conditions for the existence of the blow-up solution under the Neumman boundary and the Dirichlet boundary are obtained respectively by using the classical differential inequality. The upper bound of the “blow-up time” is estimated, and finally the concrete application of the theorem in two nonlinear problems is given.
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