An Initial–Boundary Value Problem for a Sobolev-Type Strongly Nonlinear Dissipative Equation

摘要

An initial–boundary value problem is considered for a model equation governing waves incrystalline semiconductors with allowance for strong spatial dispersion, linear dissipation, and sourcesof free charges. The weak generalized local-in-time solvability of the problem is proved. Sufficient con-ditions are obtained for the blowup of the solution and for global-in-time solvability. Two-sided esti-mates for the blowup time are derived.