On the destruction of solutions to Cauchy problems for nonlinear ferrite equations in $(N + 1)$-dimensional case

In this paper, we consider three Cauchy problems for $(N + 1)$ dimensional nonlinear Sobolev type equations arising in the theory of magnetic vibrations in ferrites. We obtain results on the existence and uniqueness of weak solutions to these problems that are local in time, as well as on the existence and uniqueness of weak solutions to these problems, and on destroying these solutions.