Abstract:

The authors studied the global existence and blow\|up properties of positive solutions of an evolution p-Laplace system
 with nonlinear inner sources and nonlinear boundary conditions. The authors first proved a local existence result by the regularization method, then  proved a weak comparison principle and finally,  obtained some necessary and sufficient conditions for the global existence of all positive weak solutions by constructing upper and lower solutions. The result shows that under the proper assumptions on initial value, the necessary and sufficient conditions for the global existence of all positive weak solutions only related to the exponents of the system(p₁,p₂,m₁₁,m₁₂,m₂₁,m₂₂,q₁,q₂).

Key words: nonlinear boundary value problem, evolution p-Laplace system, global existence, blowup