Periodic solutions of a nonlinear parabolic equation associated with the penetration of a magnetic field into a substance

We prove the existence and uniqueness of a T-periodic weak solution of the nonlinear parabolic equation ur(0,t)=ur(1,t)+h(t)u(1,t)=0 in a Sobolev space with weight. In the proof, the Galerkin method is employed. Numerical results are given.