This article deals with the global existence and blow-up of positive solution of a nonlinear diffusion equation with nonlocal source and nonlocal nonlinear boundary condition. We investigate the influence of the react...This article deals with the global existence and blow-up of positive solution of a nonlinear diffusion equation with nonlocal source and nonlocal nonlinear boundary condition. We investigate the influence of the reaction terms, the weight functions and the nonlinear terms in the boundary conditions on global existence and blow up for this equation. Moreover, we establish blow-up rate estimates under some appropriate hypotheses.展开更多
This article deals with the degenerate parabolic system with nonlinear boundary flux. By constructing the self-similar supersolution and subsolution, we obtain the critical global existence curve and the critical Fuji...This article deals with the degenerate parabolic system with nonlinear boundary flux. By constructing the self-similar supersolution and subsolution, we obtain the critical global existence curve and the critical Fujita curve for the problem. Especially for the blow-up case, it is rather technical. It comes from the construction of the so-called Zel＇dovich-Kompaneetz-Barenblatt profile展开更多
基金supported in part by NSF of China(11001189),supported by NSF of China(11371384)supported in part by NSF of Chongqing(cstc2013jcyjA0940)in part by NSF of Fuling(FLKJ,2013ABA2036)
文摘This article deals with the global existence and blow-up of positive solution of a nonlinear diffusion equation with nonlocal source and nonlocal nonlinear boundary condition. We investigate the influence of the reaction terms, the weight functions and the nonlinear terms in the boundary conditions on global existence and blow up for this equation. Moreover, we establish blow-up rate estimates under some appropriate hypotheses.
基金supported in part by NSF of China (11071266)in part by NSF project of CQ CSTC (2010BB9218)partially supported by the Educational Science Foundation of Chongqing(KJ101303) China
文摘This article deals with the degenerate parabolic system with nonlinear boundary flux. By constructing the self-similar supersolution and subsolution, we obtain the critical global existence curve and the critical Fujita curve for the problem. Especially for the blow-up case, it is rather technical. It comes from the construction of the so-called Zel＇dovich-Kompaneetz-Barenblatt profile
