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The thermistor obstacle problem with periodic data. (English) Zbl 1165.35310

Summary: The object of this paper is the study of an obstacle thermistor problem with a nonlocal term. Using the classical Lax-Milgram theorem, a result of J. L. Lions [Quelques méthodes de résolution des problemes aux limites non linéaires. (Paris) (1969; Zbl 0189.40603)] and a fixed point argument we prove existence of weak periodic solutions. Finally, by means of some a-priori estimates in Campanato’s spaces, we obtain the regularity of these solutions.

MSC:

35B10 Periodic solutions to PDEs
35D05 Existence of generalized solutions of PDE (MSC2000)
35K55 Nonlinear parabolic equations

Citations:

Zbl 0189.40603
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References:

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