Numerical modeling of quasi-steady process in conducting nondispersive medium with relaxation. (English) Zbl 1338.78021

In this paper there are obtained sufficient conditions for the existence and uniqueness of weak distributional solutions for a class of Cauchy-Dirichlet problems that arise in quasi-steady processes in conducting nondispersive media with relaxation. The proof combines variational and analytic arguments. The results are illustrated by numerical experiments.


78M10 Finite element, Galerkin and related methods applied to problems in optics and electromagnetic theory
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65J15 Numerical solutions to equations with nonlinear operators
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
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