This paper is mainly focused on the global existence and extinction behaviour of the solutions to a doubly nonlinear parabolic equation with logarithmic nonlinearity. By making use of energy estimates method and a ser...This paper is mainly focused on the global existence and extinction behaviour of the solutions to a doubly nonlinear parabolic equation with logarithmic nonlinearity. By making use of energy estimates method and a series of ordinary differential inequalities, the global existence of the solution is obtained. Moreover, we give the sufficient conditions on the occurrence(or absence)of the extinction behaviour.展开更多
We start from a super-Brownian motion with the branching mechanism presented by Dawson and Vinogradov. Its behaviour near extinction is studied in this paper, and the main result is that the diameter of the support te...We start from a super-Brownian motion with the branching mechanism presented by Dawson and Vinogradov. Its behaviour near extinction is studied in this paper, and the main result is that the diameter of the support tends to zero almost surely at the time of extinction.展开更多
基金Supported by the Project of Education Department of Hunan Province (20A174)。
文摘This paper is mainly focused on the global existence and extinction behaviour of the solutions to a doubly nonlinear parabolic equation with logarithmic nonlinearity. By making use of energy estimates method and a series of ordinary differential inequalities, the global existence of the solution is obtained. Moreover, we give the sufficient conditions on the occurrence(or absence)of the extinction behaviour.
基金Research supported by Tianyuan FoundationPostdoctoral Foundation
文摘We start from a super-Brownian motion with the branching mechanism presented by Dawson and Vinogradov. Its behaviour near extinction is studied in this paper, and the main result is that the diameter of the support tends to zero almost surely at the time of extinction.
