Dynamic singular perturbation problems for multi-structures

Abstract

This paper contains an overview of recent development in asymptotic analysis of "elds in multi-structures. We begin with simple examples of scalar dynamic problems in two dimensions, and then present analysis of time-dependent "elds in 1D}3D multi-structures. The asymptotic results, presented here, are based on the method of compound asymptotic expansions.

Seventy Five (Thousand) Unsolved Problems in Analysis and Partial Differential Equations

“…domains dependent on small parameters in such a way that the limit region, as parameters tend to zero, consists of subsets of different space dimensions. Asymptotic analysis of physical fields in multi-structures is developed in [31,77] and elsewhere. Direct methods of variational calculus are often ineffective for solving problems of optimal control of multi-structures because of their complicated geometry.…”

“…Direct methods of variational calculus are often ineffective for solving problems of optimal control of multi-structures because of their complicated geometry. However, [77,Remark 4.4] suggests the following promising Problem 75. Apply algebraic optimization methods to asymptotic approximations of fields in 1D-3D multi-structures.…”