On the global-in-time solvability of the Cauchy problem for a nonlinear equation from a semiconductor diffusion-drift model

The Cauchy problem is considered for a nonlinear Sobolev-type equation involving a p-Laplacian term in N-dimensional space (for N ≥ 3). Existence, uniqueness, and global-in-time solvability in a certain weak sense are proved for specific values ​​of the parameter p.