Solution of the nonlinear equation of a divergent type in the corner point domain

E. E. Perepelkin; B. I. Sadovnikov; N. G. Inozemtseva

doi:10.1007/s41808-018-0013-6

Solution of the nonlinear equation of a divergent type in the corner point domain

Mathematical Physics 2018-05-04 v1 math.MP

Authors: E. E. Perepelkin , B. I. Sadovnikov , N. G. Inozemtseva

View on arXiv ↗ PDF ↗ DOI ↗

Abstract

The algorithm for generation of exact solutions of the nonlinear equation in partial derivatives of a divergent type which is included in the formulation of magnetostatics, hydro-and aerodynamics, quantum mechanics (stationary Schr\"odinger equation) has been suggested. The properties of smoothness of solutions in domains with corner points (piecewise smooth boundary) have been considered. The solutions with unlimited derivatives in the corner point domain have been presented on the basis of a new class of special functions.

Keywords

nonlinear partial differential equation divergence type corner point domain exact solution special functions smoothness magnetostatics

Cite

@article{arxiv.1604.05357,
  title  = {Solution of the nonlinear equation of a divergent type in the corner point domain},
  author = {E. E. Perepelkin and B. I. Sadovnikov and N. G. Inozemtseva},
  journal= {arXiv preprint arXiv:1604.05357},
  year   = {2018}
}

Comments

29 pages, 16 figures

Solution of the nonlinear equation of a divergent type in the corner point domain

Abstract

Keywords

Cite

Comments

Related papers