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
| Annotation | 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. |
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| Keywords | dislocation 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)
