Inverse Problem for the Sobolev Type Equation of Higher Order

The article investigates the inverse problem for a complete, inhomogeneous, higher-order Sobolev type equation, together with the Cauchy and overdetermination conditions. This problem was reduced to two equivalent problems in the aggregate: regular and singular. For these problems, the theory of polynomially bounded operator pencils is used. The unknown coefficient of the original equation is restored using the method of successive approximations. The main result of this work is a theorem on the unique solvability of the original problem. This study continues and generalizes the authors’ previous research in this area. All the obtained results can be applied to the mathematical modeling of various processes and phenomena that fit the problem under study.

Numerical investigation of thegeneralized Hoff model

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.

NUMERICAL INVESTIGATION OF THE SHOWALTER - SIDOROV PROBLEM FOR NONLINEAR DIFFUSION EQUATION

The article concerns a numerical investigation of nonlinear diffusion mod- el in the circle. Nonlinear diffusion equation simulates the change of potential concentration of viscoelastic fluid, which is filtered in a porous media. This equa- tion is a semilinear Sobolev type equation. Sobolev type equations constitute a vast area of non-classical equations of mathematical physics. Theorem of exis- tence and uniqueness of a weak generalized solution to the Showalter - Sidorov problem for nonlinear diffusion equation is stated. The algorithm of numerical solution to the problem in a circle was developed using the modified Galerkin method. There is a result of computational experiment in this article.