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The thermistor problem: Existence, smoothness, uniqueness, blowup. (English) Zbl 0808.35059
Summary: The goal of this paper is to study a nonlinear system modeling the heat diffusion produced by Joule effect in an electric conductor. Existence, uniqueness, smoothness, and blowup in particular are studied.

MSC:
35K60Nonlinear initial value problems for linear parabolic equations
35K20Second order parabolic equations, initial boundary value problems
35K50Systems of parabolic equations, boundary value problems (MSC2000)
35A05General existence and uniqueness theorems (PDE) (MSC2000)
35B40Asymptotic behavior of solutions of PDE
35D10Regularity of generalized solutions of PDE (MSC2000)