摘要
This paper deals with the blow-up of positive solutions of the uniformly pa-rabolic equations ut = Lu + a(x)f(u) subject to nonlinear Neumann boundary conditions . Under suitable assumptions on nonlinear functi-ons f, g and initial data U0(x), the blow-up of the solutions in a finite time is proved by the maximum principles. Moreover, the bounds of 'blow-up time' and blow-up rate are obtained.
This paper deals with the blow-up of positive solutions of the uniformly pa-rabolic equations ut = Lu + a(x)f(u) subject to nonlinear Neumann boundary conditions . Under suitable assumptions on nonlinear functi-ons f, g and initial data U0(x), the blow-up of the solutions in a finite time is proved by the maximum principles. Moreover, the bounds of 'blow-up time' and blow-up rate are obtained.
基金
This work is partially supported by Open Project of the Defense Key Laboratory of Science and Technology(OOJS76.4.2JW0810), Talent Teacher Program of Chinese Ministry of Education and the National Science Foundation of China(60174007).
