Scientific publications

Чернов И.А.

Классическое решение краевой задачи с нелинейными граничными условиями и подвижной границей

// Методы математич. моделирования и информационные технологии. Труды ИПМИ КарНЦ РАН. Вып. 8. Петрозаводск: КарНЦ РАН, 2007. C. 48-67

Chernov L.A. Classical solution to the boundary-value problem with nonlinear boundary condition and a moving bound // Methods of mathematical modeling and information technologies. Proceedings of the Institute of Applied Mathematical Research. Volume 8. Petrozavodsk: KarRC RAS, 2007. Pp. 48-67

We consider the nonlinear Stefan-type boundary-value problem, which is a generalization of the model of hydriding under constant conditions. We construct lattice approximations for the moving bound and the unknown function and prove that they converge to continuous functions. These functions have necessary derivatives and satisfy all equations of the boundary-value problem; therefore they are the classical solution to the problem. By that we prove the existence theorem in a constructive way: the lattice method can be used for numerical solution.

Last modified: December 25, 2008