Analysis of nonlinear PDEs
(conservation laws, degenerate elliptic and parabolic problems). Theoretical numerical analysis (finite volume methods).
Main publications:
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
