Title: Disproof of a conjectured inequality arising in the theory of magnetic flux diffusion
Other Involved Persons: Book, David L.
Other Involved Persons: Brun, Todd A.
Source: Journal of Mathematical Physics, Vol. 30, No. 12 (1989), p. 2947-2950
ISSN: 1089-7658
Summary: The conjecture that the magnetic field energy introduced into an imperfectly conducting medium by diffusion is less than the thermal energy produced by the associated Joule heating is shown to imply the positivity of a certain integral operator with an indefinite kernel. Counterexamples are found by means of a variational calculation.
URL: http://dx.doi.org/10.1063/1.528482