In this paper, we consider a strongly-coupled parabolic system with initial boundary values. Under the appropriate conditions, using Gagliard-Nirenberg inequality, Poincare inequality, Gronwall inequality and imbedding theorem, we obtain the global existence of solutions.
This paper deals with the blow-up rate estimates of positive solutions for systems of heat equationswith nonlinear boundary conditions. The upper and lower bounds of blow-up rate are obtained.
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.
This paper deals with the blow-up rate estimates of solutions for semilinear parabolic systems coupled in an equation and a boundary condition. The upper and lower bounds of blow-up rates have been obtained.
This paper is devoted to study the classification of self-similar solutions to the quasilinear parabolic equations with nonlinear gradient termsu t = Δ(u m) - uq∣Δu∣ p withm ≥ 1,p,q > 0 andp +q >m. Form = 1, it is shown that the very singular self-similar solution exists if and only ifnq + (n +1)p 1, it is shown that very singular self-similar solutions exist if and only if 1
SHI Peihu & WANG MingxinDepartment of Mathematics, Southeast University, Nanjing 210018, China
