ISSN 2079-6900 (Print) 
ISSN 2587-7496 (Online)

Middle Volga Mathematical Society Journal

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On the differentiability of solutions of the liminal dissipative equation

S. N. Alekseenko1, D. V. Khiteva2

AnnotationThere 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.
Keywordsdislocation density, nonlinear first-order partial differential equation, liminality method of an additional argument

1The professor of the applied mathematics chair, Nizhniy Novgorod State Technical University, Nizhniy Novgorod; sn-alekseenko@yandex.ru

2The undergraduate of the applied mathematics chair, Nizhniy Novgorod State Technical University, Nizhniy Novgorod; geheimberater@yandex.ru

Citation: S. N. Alekseenko, D. V. Khiteva, "[On the differentiability of solutions of the liminal dissipative equation]", Zhurnal Srednevolzhskogo matematicheskogo obshchestva,17:3 (2015) 7–11 (In Russian)