On viscosity solution of functional Hamilton-Jacobi type equations for hereditary systems
On viscosity solution of functional Hamilton-Jacobi type equations for hereditary systems
复制标题
DOI：
10.1134/s0081543807060132
复制
发表时间：
2007-12
影响因子：
0.5
通讯作者：
N. Lukoyanov
中科院分区：
文献类型：
--
作者：
N. Lukoyanov
本文致力于发展具有非预期哈密顿量和余不变导数的泛函Hamilton-Jacobi型方程广义解的粘性方法。这些方程自然地与遗传系统的动力学优化问题联系在一起，与经典的哈密顿-雅可比方程相比，它们具有许多由后效规定的额外特性。给出了考虑上述特性的粘性溶液的定义。证明了这一定义与经典解的概念以及广义解的极小极大方法的一致性。证明了解的存在唯一性定理。
The paper is devoted to the development of the viscosity approach to the generalized solution of functional Hamilton-Jacobi type equations with coinvariant derivatives and a nonanticipatory Hamiltonian. These equations are naturally connected to problems of dynamical optimization of hereditary systems and, as compared with classical Hamilton-Jacobi equations, possess a number of additional peculiarities stipulated by the aftereffect. The definition of a viscosity solution that takes the above peculiarities into account is given. The consistency of this definition with the notion of a classical solution and with the minimax approach to the generalized solution is substantiated. The existence and uniqueness theorems are proved.