The Overall Presence Of Nonlinear Parabolic Equations And Blasting

In this dissertation, we study the following boundary value problem with homogeneous Dirichlet boundary condition, whereΩ(?) RN is a bounded domain with smooth boundary, p, q> 0, min{l, m}≥1,uo(x), v0(x) are nonnegtive continuous functions onΩ.The main purpose of this dissertation is to investigate the global existence and the finite time blow up of the solutions of (P).For a given solution (u(x,t),v(x,t)) we define T*= sup{T> 0:(u, v) are bounded and satisfy(P),(x, t)∈Ω×[0, T)}If T*=+(?), for all the t> 0, one has andIn this condition,we say the solution is global.If T*<+(?), one has lim sup tâ†'T* or lim sup tâ†'T* In this condition,we say the solution blows up in finite time T*.This dissertation is divided into five sections.In the first and second sections, we introduce some previous research results, as well some important definitions and propositions.In the third section, we use supersolution, the comparing principal to prove the exsistence of the global solution. In the forth section, we use subsolution, the comparing principal to prove the blow-up solution.In the fifth section, we consider the rate of blow-up solutions of the problem in special conditions and the rate of blow-up is uniform in all compact subsets of the domain.