Multidimensional system of ferro-magnetic chain type
A generalized system of ferromagnetic chain type of the form \[ z_ t= [\overset {*} g_ 1(z)\land g_ 2(z)\land\cdots\land g_{n-2}(z)\land \Delta z]+ f(x,t,z), \] where \(z= (z_ 1,\dots,z_ n)= z(x)\), \(x\in \mathbb{R}^ m\), \(t\in \mathbb{R}^ +\), \(n\geq 2\) is considered in the multidimensional case \(m\geq 1\) under the assumptions: \(g_ 1(z)\equiv z\) and \(g_ k(z)= \alpha_ k\) are linearly independent constant vectors in \(\mathbb{R}^ n\) for \(k= 2,\dots,n- 2\). With the help of Galerkin's method the global solvability of the homogeneous boundary problem for a class of multidimensional generalized systems of ferromagnetic chain type is proved.
scientific article; zbMATH DE number 541477