非线性时变广义分布参数系统的适定性问题

本文的主要目的是讨论非线性时变广义分布参数系统的适定性问题.首先,在Banach空间中引入由连续(可能是非线性的)算子引导的非线性广义发展算子,该非线性广义发展算子是广义发展算子的推广,并研究非线性广义发展算子的性质;然后,应用非线性广义发展算子讨论非线性时变广义分布参数系统的适定性问题,并给出解的构造性表达式.

Well-posed problem of nonlinear time varying singular distributed parameter systems

The main purpose of this paper is to discuss the well-posed problem of nonlinear time varying singular distributed parameter systems. First of all, the nonlinear generalized-evolution （GE-evolution） operator induced by a continuous （possibly nonlinear） operator is introduced in Banach space, which is a generalization of GE-evolution operator （i.e., generalized evolution operator）, and the properties of nonlinear GE-evolution operator are discussed; then the well-posed problem of nonlinear time varying singular distributed parameter system is discussed by nonlinear GE-evolution operator, and the constructive expression of the strong solution is obtained.