We study the existence of weak solutions to a nonlinear strongly coupled parabolic-elliptic PDEs arising in the heating induction-conduction process of steel hardening. In this setting, our major concern is to consider the case when the electric conductivity is nonuniformly elliptic which, together with a right hand side in L1 in the energy balance equation, yields to a difficult theoretical situation. The existence result gives a weak solution to a similar PDEs system where the energy balance equation has been perturbed by a measure term.
CITATION STYLE
Montesinos, M. T. G., & Gallego, F. O. (2014). Weak solutions to a nonuniformly elliptic PDE system in the harmonic regime. SEMA SIMAI Springer Series, 4, 31–39. https://doi.org/10.1007/978-3-319-06953-1_4
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