一类具有非线性边界条件的发展型p-Laplace 方程组正解的爆破性及整体存在性

考虑一类具有非线性内部源和非线性边界条件的一维发展型p-Laplace方程组正解的爆破性及整体存在性. 利用正则化方法证明了该方程组局部解的存在性和一个弱比较原理, 并通过构造上下解获得了正弱解整体存在的充分必要条件. 结果表明, 在适当的初值假设下, 正弱解整体存在的充分必要条件只与方程组的指数(p₁,p₂,m₁₁,m₁₂,m₂₁,m₂₂,q₁,q₂)有关.

Global Existence and Blow-up of Solutions to an Evolutionp-Laplace System with Nonlinear Boundary Conditions

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 (p_1 ,p_2 ,m_(11) ,m_(12) ,m_(21), m_(22) ,q_1 ,q_2 ).