Mathematics

Numerical investigation of the generalized Hoff model

N. A. Manakova, K. V. Vasyuchkova

South Ural State University, 76, Prospekt Lenina, Chelyabinsk, 454080, Russian Federation

Abstract: The work is devoted to the numerical investigation of the generalized Hoff model. Hoff equation models the dynamics of buckling construction of I-beams under a constant load. Result of existence and uniqueness of solution to the Showalter–Sidorov problem for the investigated model is formulated. This equation is a semilinear Sobolev type equation. Sobolev type equations constitute a vast area of non-classical equations of mathematical physics. Based on the theoretical results there was developed the algorithm of numerical solution of the problem.

Keywords: Hoff equation, numerical modelling, Galerkin's method, Sobolev type equations, Showalter–Sidorov problem, weak generalized solution, monotone operators, monotone method.

UDC: 517.9

Received: 18.06.2015

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