This paper deals with the blow up properties of solutions to semilinear heat equation u t- Δ u=u p in R N +×(0,T) with the nonlinear boundary condition -ο u ο x 1 = u q for x 1=0,t∈(0,T) ....This paper deals with the blow up properties of solutions to semilinear heat equation u t- Δ u=u p in R N +×(0,T) with the nonlinear boundary condition -ο u ο x 1 = u q for x 1=0,t∈(0,T) .It has been proved that if max( p,q) ≤1,every nonnegative solution is global.When min (p,q) >1 by letting α=1p-1 and β=12(q-1) it follows that if max (α,β)≥N2 ,all nontrivial nonnegative solutions are nonglobal,whereas if max (α,β)<N2 ,there exist both global and nonglobal solutions.Moreover,the exact blow up rates are established.展开更多
This paper deals with the blow-up properties of solutions to the systems ut=Δu,vt=Δv in BR × (O,T) subject to nonlinear boundary conditions δu/δη=v^p,δu/δη=u^q, in SR×(O,T). It is shown that under ce...This paper deals with the blow-up properties of solutions to the systems ut=Δu,vt=Δv in BR × (O,T) subject to nonlinear boundary conditions δu/δη=v^p,δu/δη=u^q, in SR×(O,T). It is shown that under certain conditions the solution blows up at a finite time and the blow-up only occurs on the boundary. The self-similar solution for the one-dimensional case has been studied. Moreover, the exact blow-up rates are also derived.展开更多
This paper deals with the existence and nonexistence of global positive solution of the following equation:where p, q, m, α are parameters with is a bounded domain with Ω smooth enough, The necessary and sufficient ...This paper deals with the existence and nonexistence of global positive solution of the following equation:where p, q, m, α are parameters with is a bounded domain with Ω smooth enough, The necessary and sufficient conditions for the global existence of solution are obtained.展开更多
In this paper, the authors deal with the non-constant positive steady-states of a predator-prey-mutualist model with homogeneous Neumann boundary condition. They first give a priori estimates (positive upper and lower...In this paper, the authors deal with the non-constant positive steady-states of a predator-prey-mutualist model with homogeneous Neumann boundary condition. They first give a priori estimates (positive upper and lower bounds) of positive steady-states,and then study the non-existence, the global existence and bifurcation of non-constant positive steady-states as some parameters are varied. Finally the asymptotic behavior of such solutions as d3 →∞ is discussed.展开更多
文摘This paper deals with the blow up properties of solutions to semilinear heat equation u t- Δ u=u p in R N +×(0,T) with the nonlinear boundary condition -ο u ο x 1 = u q for x 1=0,t∈(0,T) .It has been proved that if max( p,q) ≤1,every nonnegative solution is global.When min (p,q) >1 by letting α=1p-1 and β=12(q-1) it follows that if max (α,β)≥N2 ,all nontrivial nonnegative solutions are nonglobal,whereas if max (α,β)<N2 ,there exist both global and nonglobal solutions.Moreover,the exact blow up rates are established.
文摘This paper deals with the blow-up properties of solutions to the systems ut=Δu,vt=Δv in BR × (O,T) subject to nonlinear boundary conditions δu/δη=v^p,δu/δη=u^q, in SR×(O,T). It is shown that under certain conditions the solution blows up at a finite time and the blow-up only occurs on the boundary. The self-similar solution for the one-dimensional case has been studied. Moreover, the exact blow-up rates are also derived.
文摘This paper deals with the existence and nonexistence of global positive solution of the following equation:where p, q, m, α are parameters with is a bounded domain with Ω smooth enough, The necessary and sufficient conditions for the global existence of solution are obtained.
基金Project supported by the National Natural Science Foundation of China (No.19831060) the 333 Project of Jiangsu Province of China.
文摘In this paper, the authors deal with the non-constant positive steady-states of a predator-prey-mutualist model with homogeneous Neumann boundary condition. They first give a priori estimates (positive upper and lower bounds) of positive steady-states,and then study the non-existence, the global existence and bifurcation of non-constant positive steady-states as some parameters are varied. Finally the asymptotic behavior of such solutions as d3 →∞ is discussed.
