This paper discusses the global existence and quenching of the solution to the Newton filtration equation with the nonlinear boundary condition. The authors also discuss the profile of the quenching solution in the qu...This paper discusses the global existence and quenching of the solution to the Newton filtration equation with the nonlinear boundary condition. The authors also discuss the profile of the quenching solution in the quenching time and obtain the quenching rate of the quenching solution.展开更多
In this paper,we study a simplified Othmer-Stevens model with reproduction term.By making use of a smart function transformation,the comparative method and some special mathe-matical analysis,we prove the existence of...In this paper,we study a simplified Othmer-Stevens model with reproduction term.By making use of a smart function transformation,the comparative method and some special mathe-matical analysis,we prove the existence of global,blow-up or quenching solutions of the problem on different conditions.More interesting results are reached.The result of the paper not only verifies a real biological phenomenon,but also provides a theo-retical groundwork for numerical problems of the chemotaxis model.展开更多
This paper is concerned with the quenching problem of a degenerate functional reaction-diffusion equation. The quenching problem and global existence of solution for the reaction-diffusion equation are derived and, so...This paper is concerned with the quenching problem of a degenerate functional reaction-diffusion equation. The quenching problem and global existence of solution for the reaction-diffusion equation are derived and, some results of the positive steady state solutions for functional elliptic boundary value are also presented.展开更多
文摘This paper discusses the global existence and quenching of the solution to the Newton filtration equation with the nonlinear boundary condition. The authors also discuss the profile of the quenching solution in the quenching time and obtain the quenching rate of the quenching solution.
基金Supported by the National Natural Science Foundation of China(10471108)
文摘In this paper,we study a simplified Othmer-Stevens model with reproduction term.By making use of a smart function transformation,the comparative method and some special mathe-matical analysis,we prove the existence of global,blow-up or quenching solutions of the problem on different conditions.More interesting results are reached.The result of the paper not only verifies a real biological phenomenon,but also provides a theo-retical groundwork for numerical problems of the chemotaxis model.
基金This work is supported by EDSF of Shandong Province (J04A11).
文摘This paper is concerned with the quenching problem of a degenerate functional reaction-diffusion equation. The quenching problem and global existence of solution for the reaction-diffusion equation are derived and, some results of the positive steady state solutions for functional elliptic boundary value are also presented.
