Asymptotology

About: Asymptotology is a research topic. Over the lifetime, 1319 publications have been published within this topic receiving 35831 citations.

Asymptotic behaviour of solutions of boundary-value problems for equations with rapidly oscillating coefficients in a domain with a small cavity

Abstract: Asymptotic representations of the solutions of boundary-value problems for a second-order equation with rapidly oscillating coefficients in a domain with a small cavity (of diameter comparable with the period of oscillation) are found and substantiated. Dirichlet or Neumann conditions are set at the boundary of the domain. In addition to an asymptotic series of structure standard for homogenization theory there occur terms describing the boundary layer phenomenon near the opening, while the solutions of the homogenized problem and their rapidly oscillating correctors acquire singularities at the contraction point of the openings. The dimension of the domain and some other factors influence even the leading term of the asymptotic formula. Some generalizations, including ones to the system of elasticity theory, are discussed.

Asymptotics of the solution to the Neumann problem with a delta-function-like boundary function

Abstract: A uniform asymptotic expansion is found for the integral ∫∫s▽2udxdy, where u is the solution of the Neumann problem with a delta-function-like derivative on the boundary. A physics application of the result is discussed.

Momentum from sample paths in stochastic mechanics

Abstract: According to Shucker’s analysis, quantum-mechanical momentum can be read from the asymptotic behaviour of Nelson’s sample paths. Here we use the position-momentum uncertainty product as a measure of the rate of approach to the large time asymptotics.