Existence of global weak solutions for a class of quasilinear equations describing Joule's heating

Bień, Marian

doi:10.1002/(sici)1099-1476(199910)22:15<1275::aid-mma39>3.0.co;2-7

Math. Meth. Appl. Sci.

1999

DOI: 10.1002/(sici)1099-1476(199910)22:15<1275::aid-mma39>3.0.co;2-7

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Existence of global weak solutions for a class of quasilinear equations describing Joule's heating

Marian Bień

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2006

2024

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Cited by 3 publications

References 16 publications

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

Yin

2006

Math Methods in App Sciences

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SUMMARYThis paper deals with Maxwell's equations with a thermal e ect, 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 H older 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.

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

Yin

2006

Math Methods in App Sciences

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A numerical scheme for solving an induction heating problem with moving non-magnetic conductor

Le,

Slodička,

Van Bockstal

2024

Computers & Mathematics with Applications

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Existence of a weak solution to a nonlinear induction hardening problem with Leblond–Devaux model for a steel workpiece

Le¹,

Slodička²,

Bockstal³

2022

Communications in Nonlinear Science and Numerical Simulation

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Existence of global weak solutions for a class of quasilinear equations describing Joule's heating

Cited by 3 publications

References 16 publications

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

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

A numerical scheme for solving an induction heating problem with moving non-magnetic conductor

Existence of a weak solution to a nonlinear induction hardening problem with Leblond–Devaux model for a steel workpiece

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