The nonstationary dissipative first-order partial differential equation of the dislocation density with a quadratic non-linearity

Variants of hypotheses on characteristics of sinks and sources of the dislocation density in the problem of calculating the diffusion creep are considered. A first-order partial differential equation with a quadratic non-linearity in the constant term is obtained. Conditions of the local solvability and non-local boundedness of the solution and its first derivatives are determined with using the method of an additional argument.