Initial-boundary value problems for a class of systems of semilinear parabolicequations with singular terms are investigated, conditions for the existence and nonexistence of the global solutions to the above problems...Initial-boundary value problems for a class of systems of semilinear parabolicequations with singular terms are investigated, conditions for the existence and nonexistence of the global solutions to the above problems are given, and upper bounds of thequenching time and the critical length are obtained.展开更多
In this paper we consider the finite time quenching behavior of solutions to a semilinear heat equation with a nonlinear Neumann boundary condition. Firstly, we establish conditions on nonlinear source and boundary to...In this paper we consider the finite time quenching behavior of solutions to a semilinear heat equation with a nonlinear Neumann boundary condition. Firstly, we establish conditions on nonlinear source and boundary to guarantee that the solution doesn＇t quench for all time. Secondly, we give sufficient conditions on data such that the solution quenches in finite time, and derive an upper bound of quenching time. Thirdly, undermore restrictive conditions, we obtain a lower bound of quenching time. Finally, we give the exact bounds of quenching time of a special example.展开更多
文摘Initial-boundary value problems for a class of systems of semilinear parabolicequations with singular terms are investigated, conditions for the existence and nonexistence of the global solutions to the above problems are given, and upper bounds of thequenching time and the critical length are obtained.
文摘In this paper we consider the finite time quenching behavior of solutions to a semilinear heat equation with a nonlinear Neumann boundary condition. Firstly, we establish conditions on nonlinear source and boundary to guarantee that the solution doesn＇t quench for all time. Secondly, we give sufficient conditions on data such that the solution quenches in finite time, and derive an upper bound of quenching time. Thirdly, undermore restrictive conditions, we obtain a lower bound of quenching time. Finally, we give the exact bounds of quenching time of a special example.
