Existence and regularity of a weak solution to Maxwell's equations with a thermal effect

• Published in: Mathematical methods in the applied sciences Vol. 29; no. 10; pp. 1199 - 1213
• Main Author: Yin, Hong-Ming
• Format: Journal Article
• Language: English
• Published: Chichester, UK John Wiley & Sons, Ltd 10.07.2006; Wiley; Teubner
• Subjects: Exact sciences and technology; existence; Mathematical analysis; Mathematics; Maxwell's equations; Partial differential equations; Sciences and techniques of general use; thermal effect; uniqueness and regularity of solution; Solution uniqueness; Weak solution; Thermal effect; Applied mathematics; Solution regularity; existence; Thermal conductivity; Maxwell's equations; uniqueness and regularity of solution; Maxwell equation; Global solution
• ISSN: 0170-4214; 1099-1476
• DOI: 10.1002/mma.723

This paper deals with Maxwell's equations with a thermal effect, where the electric conductivity strongly depends on the temperature. It is shown that the coupled system has a global weak solution and the temperature is Hölder continuous if the conductivity decays suitably as temperature increases. Moreover, uniqueness of the solution is proved, which gives a positive answer for a open question from the previous research. The main idea for the global existence is based on deriving various energy estimates for the solution of the coupled system. Copyright © 2006 John Wiley & Sons, Ltd.