The results of experimental and theoretical study of magnetic domain structure drift in low frequency oscillating magnetic eld oriented perpendicular to the sample plate are presented. Experimental study was performed on uniaxial iron garnet (TbErGd)3(FeAl)5O12 (111) plate with rhombic anisotropy for the case when orientation of domain walls of stripe domains is preserved. Dynamic domain structure was revealed by means of magnetooptic Faraday e ect and registered by high speed digital camera at the speed equal to 1200 fps. Theoretical model based on the motion equations for coupled harmonic oscillators that takes into account attenuation and eld inhomogeneity along the plate is proposed.

A coefficient inverse problem for the non-stationary single-speed transport equation for t ∈ (0, T ) with the lateral boundary data and initial condition at t = 0 is considered. Global uniqueness result is obtained by the method of Carleman estimates.

The Lipschitz stability estimate for the non-stationary single-speed transport equation with the lateral boundary data is obtained. The method of Carleman estimates is used. Uniqueness of the solution follows. IntroductionThis paper addresses the question of the Lipschitz stability for the non-stationary single-speed transport equation with the lateral boundary data. This is a non-standard problem for such equation. The author plans to use this estimate for establishing a stability estimate for a coefficient inverse problem for this equation. The author is not aware about other publications with similar results for the non-stationary transport equation. Reviews of uniqueness and stability results for non-standard Cauchy problems for partial differential equations (PDEs) can be found in, e. g., books of Lavrentev, Romanov, Shishatskii [10], Ames and Straughan [1], Isakov [6], and Klibanov and Timonov [9]. A derivation of the transport equation for non-stationary case can be found, for example, in the book of Case and Zweifel [4].The proof of the main result of this paper is based on a new Carleman estimate. Traditionally, Carleman estimates have been used for proof of stability and uniqueness results for non-standard Cauchy problems for PDEs. They were first introduced by Carleman in 1939 [3], also see Hörmander [5], and [10], [6], [9]. Since the work of Bukhgeim and Klibanov [2] Carleman estimates are also used for proofs of uniqueness and stability results for coefficient inverse problems and, most recently, for construction of numerical methods, see the book of Klibanov and Timonov [9] for details and more references. Works of Klibanov and Malinsky [8] and Kazemi and Klibanov [7] were the first ones, where Carleman estimates were used for proofs of the Lipschitz stability estimates for hyperbolic equations with lateral Cauchy data; also see [9]. The method of this paper is similar with one of [9], [7] and [8]. In Section 2 the statements of the results are given; in Section 3 the proofs of these results are provided. Statements of results Denote

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The results of study of domain walls oscillations in harmonic magnetic field H = H0sin (2πft) oriented perpendicular to ferrite garnet (TbErGd)3(FeAl)5O12 (111) sample plate for amplitudes that include the drift of domain walls are reported. Numerical modelling of domain walls motion was performed for frequencies f~102 Hz, where the drift is observed experimentally. Comparison of results of numerical modelling with experimental results shows their qualitative agreement. It was established that domain walls oscillations amplitude is a linear function of amplitude of oscillating magnetic field.