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Autor:
Chemetov, N. V.
Publikováno v:
Communications on Pure and Applied Analysis, 10 (4) (2011), 1079-1096
In the article we study a hyperbolic-elliptic system of PDE. The system can describe two different physical phenomena: 1st one is the motion of magnetic vortices in the II-type superconductor and 2nd one \ is the collective motion of cells. Motivated
Externí odkaz:
http://arxiv.org/abs/2409.17097
Autor:
Popov, I. S.
Numerical methods of the ADER family, in particular finite-element ADER-DG and finite-volume ADER-WENO methods, are among the most accurate numerical methods for solving quasilinear PDE systems. The internal structure of ADER-DG and ADER-WENO numeric
Externí odkaz:
http://arxiv.org/abs/2409.12483
We introduce estimatable variation neural networks (EVNNs), a class of neural networks that allow a computationally cheap estimate on the $BV$ norm motivated by the space $BMV$ of functions with bounded M-variation. We prove a universal approximation
Externí odkaz:
http://arxiv.org/abs/2409.08909
Autor:
Samantaray, Saurav
We consider the compressible Euler equations of gas dynamics with isentropic equation of state. Standard numerical schemes for the Euler equations suffer from stability and accuracy issues in the low Mach regime. These failures are attributed to the
Externí odkaz:
http://arxiv.org/abs/2409.05854
Autor:
Rozanova, Olga S.
The spatial dimensions 1 and 4 play an exceptional role for radial solutions of the pressureless repulsive Euler-Poisson equations. Namely, for any spatial dimension except 1 and 4, any nontrivial solution of the Cauchy problem blows up in a finite t
Externí odkaz:
http://arxiv.org/abs/2408.13794
Multi-component Baer-Nunziato-type models for isothermal and isentropic fluids are investigated. These are given by balance equations for volume fractions, density and momentum for each component accounting for the relaxation to equilibrium by means
Externí odkaz:
http://arxiv.org/abs/2407.06919
In the present work, an approach to the moment closure problem on the basis of orthogonal polynomials derived from Gram matrices is proposed. Its properties are studied in the context of the moment closure problem arising in gas kinetic theory, for w
Externí odkaz:
http://arxiv.org/abs/2407.05894
In this work, we develop a new hydrostatic reconstruction procedure to construct well-balanced schemes for one and multilayer shallow water flows, including wetting and drying. Initially, we derive the method for a path-conservative finite volume sch
Externí odkaz:
http://arxiv.org/abs/2406.14119
Autor:
Ho, Andrew, Shumlak, Uri
The two-fluid plasma model has a wide range of timescales which must all be numerically resolved regardless of the timescale on which plasma dynamics occurs. The answer to solving numerically stiff systems is generally to utilize unconditionally stab
Externí odkaz:
http://arxiv.org/abs/2405.02182
Autor:
Glass, Olivier
In this paper, we consider $2 \times 2$ hyperbolic systems of conservation laws in one space dimension with characteristic fields satisfying a condition that encompasses genuine nonlinearity and linear degeneracy as well as intermediate cases, namely
Externí odkaz:
http://arxiv.org/abs/2405.02123