Abstract:
There is established the conditions under which the solutions of the liminal dissipative equation have third derivatives with respect to the spatial variables. As principal conditions for a prolongation of solutions are formulated for the second derivatives, the equation for the second derivative of a solution to considered problem is constructed. The peculiarity of this equation is that its in the extended characteristic system has a convenient to deducing of global estimates form.
Keywords:dislocation density, nonlinear first-order partial differential equation, liminality method of an additional argument.