A scalar prototype problem of deep abrasive drilling with an infinite free boundary : an asymptotic modeling study

• A vanishing at infinity solution of the three-dimensional Laplace equation is sought in an a priori unknown domain with overdetermined boundary conditions, the right-hand sides of which depend on the unit normal to the free boundary. A perturbation analysis of the nonstandard free boundary problem that models deep abrasive drilling has been performed under the assumption that the free boundary is close to the surface of a given semi-infinite cylinder, the longitudinal position of which depends on the boundary data, and the leading-order asymptotic solution has been developed.

Subject headings

NATURVETENSKAP  -- Matematik -- Matematisk analys (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Mathematical Analysis (hsv//eng)

Keyword

Free boundary

Perturbation analysis

Linearized free boundary problem

Publication and Content Type

ref (subject category)

art (subject category)