NUMERICAL MODELING OF QUASI-STEADY PROCESS IN CONDUCTING NONDISPERSIVE MEDIUM WITH RELAXATION

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Published: May 10, 2015
Keywords:
Galerkin method quasi-linear Sobolev type equation weak generalized solution numerical modeling.

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Ekaterina Bogatyreva
South Ural State University

Abstract

Sufficient conditions of existence and uniqueness of weak generalized solution to the Dirichlet--Cauchy problem for equation modeling a quasi-steady process in conducting nondispersive medium with relaxation are obtained. The main equation of the model is considered as a representative of the class of quasi-linear equations of Sobolev type. It enables to prove a solvability of the Dirichlet--Cauchy problem in a weak generalized meaning by methods developed for this class of equations. In suitable functional spaces the Dirichlet--Cauchy problem is reduced to the Cauchy problem for abstract quasi-linear operator differential equation of the special form. Algorithm of numerical solution to the Dirichlet--Cauchy problem based on the Galerkin method is developed. Results of computational experiment are provided.

Article Details

Issue
Vol. 2 No. 1 (2015): JOURNAL OF COMPUTATIONAL AND ENGINEERING MATHEMATICS
Section
Survey Articles
Author Biography

Ekaterina Bogatyreva, South Ural State University

Postgraduate student, Department of Equation of Mathematical Physics

References

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