【摘要】 利用Galerkin方法证明一类非线性抛物—常微弱耦合方程组混合问题广义解的存在性、唯一性和该混合问题的积分模估计;通过广义上、下解方法、Soblev嵌入定理及归纳法证明极大序列和极小序列分别是单调不增和单调不减的;由勒贝格控制收敛定理及Gronwall不等式严格证明了极大序列和极小序列分别从上方和下方单调收敛于问题的唯一广义解.更多还原

【Abstract】 A mixed problem of the nonlinear weakly coupled parabolic and ordinary system is discussed.The existence,uniqueness and the estimation of integral norm of the mixed problem is proved by Galerkin method.It is verified that maximizing sequence and minimizing sequence is monotone nonincreasing and nondecreasing respectively by using the method of generalized upper and lower solution,Soblev embedding theorem and induction method.It has furthermore established that they converge to the unique generalized solution of the problem from the upper and lower by using Lebesgue control-convergent theorem and Gronwall inequality.更多还原