7 citations · 25 across the 10 of their papers we have counts for
6 papers · 2 filters
Convergence of Variational Approximation Schemes for Elastodynamics with Polyconvex Energy
Alexey Miroshnikov, Athanasios E. Tzavaras
We consider a variational scheme developed by S. Demoulini, D. M. A. Stuart and A. E. Tzavaras [Arch. Ration. Mech. Anal. 157 (2001)] that approximates the equations of three dimen…
Relative entropy in hyperbolic relaxation for balance laws
Alexey Miroshnikov, Konstantina Trivisa
We present a general framework for the approximation of systems of hyperbolic balance laws. The novelty of the analysis lies in the construction of suitable relaxation systems and…
A variational approximation scheme for radial polyconvex elasticity that preserves the positivity of Jacobians
Alexey Miroshnikov, Athanasios E. Tzavaras
We consider the equations describing the dynamics of radial motions for isotropic elastic materials; these form a system of non-homogeneous conservation laws. We construct a variat…
Stability and Convergence of Relaxation Schemes to Hyperbolic Balance Laws via a Wave Operator
Alexey Miroshnikov, Konstantina Trivisa
This article deals with relaxation approximations of nonlinear systems of hyperbolic balance laws. We introduce a class of relaxation schemes and establish their stability and conv…
The problem of dynamic cavitation in nonlinear elasticity
Jan Giesselmann, Alexey Miroshnikov, Athanasios E. Tzavaras
The notion of singular limiting induced from continuum solutions (slic-solutions) is applied to the problem of cavitation in nonlinear elasticity, in order to re-assess an example…
On the construction and properties of weak solutions describing dynamic cavitation
Alexey Miroshnikov, Athanasios E. Tzavaras
We consider the problem of dynamic cavity formation in isotropic compressible nonlinear elastic media. For the equations of radial elasticity we construct self-similar weak solutio…