with Neumann boundary conditions. We show that the solutions of the model are bounded all the time for each pair of initial values if r>p-1 and rq>(p-1)(s-1), and that they will blow up in a finite time for some...with Neumann boundary conditions. We show that the solutions of the model are bounded all the time for each pair of initial values if r>p-1 and rq>(p-1)(s-1), and that they will blow up in a finite time for some initial values if either r>p-1 with rq<(p-1)(s+1) or r<p-1.展开更多
We study the global (in time) existence of nonnegative solutions of the Gierer-Meinhardt system with mixed boundary conditions. In the research, the Robin boundary and Neumann boundary conditions were used on the acti...We study the global (in time) existence of nonnegative solutions of the Gierer-Meinhardt system with mixed boundary conditions. In the research, the Robin boundary and Neumann boundary conditions were used on the activator and the inhibitor conditions respectively. Based on the priori estimates of solutions, the considerable results were obtained.展开更多
This paper deals with the existence and nonexistence of global positive solutions of initial and boundary value problem for the general activator-inhibitor model In this paper, we do not restrict ourselves to the init...This paper deals with the existence and nonexistence of global positive solutions of initial and boundary value problem for the general activator-inhibitor model In this paper, we do not restrict ourselves to the initial data 1/uo, 1/uo ∈L∞(Ω). We prove that there exist glolal solutions if 0 ≤ u0 ≤ u0 and they will blow up in finite time if 0 ≤ v0 ＜ u0 whether u0, v0 are small or large.展开更多
文摘with Neumann boundary conditions. We show that the solutions of the model are bounded all the time for each pair of initial values if r>p-1 and rq>(p-1)(s-1), and that they will blow up in a finite time for some initial values if either r>p-1 with rq<(p-1)(s+1) or r<p-1.
文摘We study the global (in time) existence of nonnegative solutions of the Gierer-Meinhardt system with mixed boundary conditions. In the research, the Robin boundary and Neumann boundary conditions were used on the activator and the inhibitor conditions respectively. Based on the priori estimates of solutions, the considerable results were obtained.
文摘This paper deals with the existence and nonexistence of global positive solutions of initial and boundary value problem for the general activator-inhibitor model In this paper, we do not restrict ourselves to the initial data 1/uo, 1/uo ∈L∞(Ω). We prove that there exist glolal solutions if 0 ≤ u0 ≤ u0 and they will blow up in finite time if 0 ≤ v0 ＜ u0 whether u0, v0 are small or large.
