Geodesic
Numerical modeling of quasi-steady process in conducting nondispersive medium with relaxation
Journal of computational and engineering mathematics, Tome 2 (2015) no. 1, pp. 45-51.

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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.
Keywords: Galerkin method, quasi-linear Sobolev type equation, weak generalized solution, numerical modeling. 
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E. A. Bogatyreva. Numerical modeling of quasi-steady process in conducting nondispersive medium with relaxation. Journal of computational and engineering mathematics, Tome 2 (2015) no. 1, pp. 45-51. http://geodesic.mathdoc.fr/item/JCEM_2015_2_1_a4/

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