### Abstract

We study asymptotic solutions of a Cauchy problem for induction equations describing magnetic field in a well conducting fluid. We assume that the coefficient (the velocity field of the fluid) changes rapidly in a small vicinity of a two-dimensional surface. We prove that the weak limit of the solution has delta-type singularity on this surface; in the case of a perfectly conducting fluid, we describe several regularizations of the problem with discontinuous coefficients which allow to define generalized solutions.

**Key words:** Induction equation, Cauchy problem, generalized solutions.

### Full Text

### Article Information

Title | Delta-type solutions for a system of induction equations with discontinuous velocity field |

Source | Methods Funct. Anal. Topology, Vol. 20 (2014), no. 1, 17-33 |

MathSciNet |
MR3242120 |

zbMATH |
1313.35335 |

Milestones | Received 10/10/2013 |

Copyright | The Author(s) 2014 (CC BY-SA) |

### Authors Information

*A. I. Esina*

A.Yu. Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences, Moscow, Russia

*A. I. Shafarevich*

M.V. Lomonosov Moscow State University, Moscow, Russia

### Citation Example

A. I. Esina and A. I. Shafarevich, *Delta-type solutions for a system of induction equations with discontinuous velocity field*, Methods Funct. Anal. Topology **20**
(2014), no. 1, 17-33.

### BibTex

@article {MFAT714,
AUTHOR = {Esina, A. I. and Shafarevich, A. I.},
TITLE = {Delta-type solutions for a system of induction equations with discontinuous velocity field},
JOURNAL = {Methods Funct. Anal. Topology},
FJOURNAL = {Methods of Functional Analysis and Topology},
VOLUME = {20},
YEAR = {2014},
NUMBER = {1},
PAGES = {17-33},
ISSN = {1029-3531},
MRNUMBER = {MR3242120},
ZBLNUMBER = {1313.35335},
URL = {http://mfat.imath.kiev.ua/article/?id=714},
}