conservation laws and systems,
degenerate parabolic equations,
Leray-Lions operators,
entropy and renormalized solutions,
finite volume methods.
Коды УДК:
517.956.35
Основные темы научной работы
Analysis of nonlinear PDEs
(conservation laws, degenerate elliptic and parabolic problems). Theoretical numerical analysis (finite volume methods).
Основные публикации:
B. P. Andreianov, Ph. Benilan, S. N. Kruzhkov, “$L^1$-theory of scalar conservation law with continuous flux function”, J. Funct. Anal., 171:1 (2000), 15–33
B. P. Andreyanov, “On limits of solutions of the Riemann problem for a system of isentropic gas dynamics with viscosity in Euler coordinates”, Mat. Sbornik, 194:6 (2003), 3–22
B. A. Andreianov, M. Gutnic, P. Wittbold, “Convergence of finite volume approximations for a nonlinear elliptic-parabolic problem: a “continuous” approach”, SIAM J. Numer. Anal., 42:1 (2004), 228–251
B. Andreianov, F. Boyer, F. Hubert, “Discrete duality finite volume schemes for Leray-Lions-type elliptic problems on general 2D meshes”, Numer. Methods Partial Differential Equations, 23:1 (2007), 145–195
B. P. Andreianov, N. Igbida, “Uniqueness for inhomogeneous Dirichlet problem for elliptic-parabolic equations”, Proc. Royal Soc. Edinburgh Sect. A, 137:6 (2007), 1119–1133
Б. П. Андреянов, “О пределах решений задачи Римана для системы
изэнтропической газовой динамики
с вязкостью в эйлеровых координатах”, Матем. сб., 194:6 (2003), 3–22; B. P. Andreianov, “On viscous limit solutions of the Riemann problem for the equations of isentropic gas dynamics in Eulerian coordinates”, Sb. Math., 194:6 (2003), 793–811
Б. П. Андреянов, “Метод исчезающей вязкости и явное решение задачи Римана для скалярного закона сохранения”, Вестн. Моск. ун-та. Сер. 1. Матем., мех., 1999, № 1, 3–8
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