相关论文: Weak entropy solutions to a model in induction har…

The theory of finite and infinitary term rewriting is extensively developed for orthogonal rewrite systems, but to a lesser degree for weakly orthogonal rewrite systems. In this note we present some contributions to the latter case of weak…

We consider a strongly nonlinear PDE system describing solid-solid phase transitions in shape memory alloys. The system accounts for the evolution of an order parameter (related to different symmetries of the crystal lattice in the phase…

We propose a framework for unified analysis of mixed methods for elasticity with weakly symmetric stress. Based on a commuting diagram in the weakly symmetric elasticity complex and extending a previous stability result, stable mixed…

Alternative approach for description of the non-equilibrium phenomena arising in solids at a severe external loading is analyzed. The approach is based on the new form of kinetic equations in terms of the internal and modified free energy.…

To verify theoretical results it is sometimes important to use a numerical example where the solution has a particular regularity. The paper describes one approach to construct such examples. It is based on the regularity theory for…

We consider a weak adversarial network approach to numerically solve a class of inverse problems, including electrical impedance tomography and dynamic electrical impedance tomography problems. We leverage the weak formulation of PDE in the…

Volume-filling cross-diffusion equations for the components of a tissue structure are formally derived from mass conservation laws and force balances for the interphase pressures and viscous drag forces in a multiphase approach. The…

We present a weak finite element method for elliptic problems in one space dimension. Our analysis shows that this method has more advantages than the known weak Galerkin method proposed for multi-dimensional problems, for example, it has…

A class of stochastic parabolic equations with singular potentials is analysed in the chaos expansion setting where the Wick product is used to give sense to the product of generalized stochastic processes. For the analysis of such…

In this article, the weak-strong uniqueness principle is proved for an Euler-Poisson system in the whole space, with initial data so that the strong solution exists. Some results on Riesz potentials are used to justify the considered weak…

Solutes added to solutions often dramatically impact molecular processes ranging from the suspension or precipitation of colloids to biomolecular associations and protein folding. Here we revisit the origins of the effective attractive…

We study the weak solutions to the electron-MHD system and obtain a conditional uniqueness result. In addition, we prove conservation of helicity for weak solutions to the electron-MHD system under a geometric condition.

This paper examines the decay properties of positive solutions for a family of fully nonlinear systems of integral equations containing Wolf potentials and Hardy weights. This class of systems includes examples which are closely related to…

The aim of this article is to investigate the well-posedness, stability and convergence of solutions to the time-dependent Maxwell's equations for electric field in conductive media in continuous and discrete settings. The situation we…

For an SDE driven by a rotationally invariant $\alpha$-stable noise we prove weak uniqueness of the solution under the balance condition $\alpha+\gamma>1$, where $\gamma$ denotes the Holder index of the drift coefficient. We prove existence…

The paper is concerned with the analysis of an evolutionary model for magnetoviscoelastic materials in two dimensions. The model consists of a Navier-Stokes system featuring a dependence of the stress tensor on elastic and magnetic terms, a…

Incremental methods are widely utilized for solving finite-sum optimization problems in machine learning and signal processing. In this paper, we study a family of incremental methods -- including incremental subgradient, incremental…

This article studies the uniqueness of the weak solution of the incompressible Navier-Stokes Equations in the 3-dimensional case. Here, the investigation is provided using two different approaches. The first (the main) result is obtained…

High entropy alloys (HEA) represent a class of materials with promising properties, such as high strength and ductility, radiation damage tolerance, etc. At the same time, a combinatorially large variety of compositions and a complex…

A classical model for sources and sinks in a two-dimensional perfect incompressible fluid occupying a bounded domain dates back to Yudovich in 1966. In this model, on the one hand, the normal component of the fluid velocity is prescribed on…