The study of small magnetic particles has become a very important topic, in particular for the development of technological devices such as those used for magnetic recording. In this field, switching the magnetization inside the magnetic sample is of particular relevance. We here investigate mathematically this problem by considering the full partial differential model of Landau-Lifschitz equations triggered by a uniform (in space) external magnetic field.

The study of small magnetic particles has become a very important topic, in particular for the development of technological devices such as those used for magnetic recording. In this field, switching the magnetization inside the magnetic sample is of particular relevance. We here investigate mathematically this problem by considering the full partial differential model of Landau-Lifschitz equations triggered by a uniform (in space) external magnetic field.

Several abstract model problems of elliptic and parabolic type with inhomogeneous initial and boundary data are discussed. By means of a variant of the Dore-Venni theorem, real and complex interpolation, and trace theorems, optimal $L_p$-regularity is shown. By means of this purely operator theoretic approach, classical results on $L_p$-regularity of the diffusion equation with inhomogeneous Dirichlet or Neumann or Robin condition are recovered. An application to a dynamic boundary value problem with surface...

Reiterated homogenization is studied for divergence structure parabolic problems of the form $\partial u_{\epsilon }/\partial t-div\left(a\left(x,x/\epsilon ,x/{\epsilon }^2,t,t/{\epsilon }^k\right)\nabla u_{\epsilon }\right)=f$. It is shown that under standard assumptions on the function $a(x,y_1,y_2,t,\tau )$ the sequence $\left\{u_{ϵ}\right\}$ of solutions converges weakly in $L^2(0,T;H_0^1\left(\Omega \right))$ to the solution $u$ of the homogenized problem $\partial u/\partial t-div\left(b\right(x,t\left)\nabla u\right)=f$.