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

S.N. Alekseenko1, S.N. Nagornykh2, N. S. Alekseenko3

AnnotationVariants 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.
Keywordsdislocation density, nonlinear first-order equation, local solvability, method of an additional argument, boundedness.

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

2The senior lecture of the theoretical physics chair, Nizhniy Novgorod State Pedagogical University, Nizhniy Novgorod; algoritm@sandy.ru

3The senior software developer, Intel, Nizhniy Novgorod; nik-alekseenko@yandex.ru

Citation: S.N. Alekseenko, S.N. Nagornykh, N. S. Alekseenko, "[The nonstationary dissipative first-order partial differential equation of the dislocation density with a quadratic non-linearity]", Zhurnal Srednevolzhskogo matematicheskogo obshchestva,14:2 (2012) 15–21 (In Russian)