Open Access

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

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.

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},
}