Related papers: Symmetric form of governing equations for capillar…
A thermodynamically consistent framework able to model either diffusive and displacive phase transitions is proposed. The first law of thermodynamics, the balance of linear momentum equation and the Cahn-Hilliard equation for solute mass…
Integrable velocity-dependent constraints are said to be semiholonomic. For good reasons, holonomic and semiholonomic constraints are thought to be indistinguishable in Lagrangian mechanics. This well-founded belief notwithstanding, here we…
In this paper, we present a new model for heat transfer in compressible fluid flows. The model is derived from Hamilton's principle of stationary action in Eulerian coordinates, in a setting where the entropy conservation is recovered as an…
We investigate the role of generalized symmetries in driving non-equilibrium and non-linear phenomena, specifically focusing on turbulent systems. While conventional turbulence studies have revealed inverse cascades driven by conserved…
We consider a system of nonlinear partial differential equations describing the motion of an incompressible chemically reacting generalized Newtonian fluid in three space dimensions. The governing system consists of a steady…
We consider a class of abstract quasilinear parabolic problems with lower--order terms exhibiting a prescribed singular structure. We prove well--posedness and Lipschitz continuity of associated semiflows. Moreover, we investigate global…
We study a class of variational problems for regularized conservation laws with Lax's entropy-entropy flux pairs. We first introduce a modified optimal transport space based on conservation laws with diffusion. Using this space, we…
We study the general properties of dissipative fluid distributions endowed with hyperbolical symmetry. Their physical properties are analyzed in detail. It is shown that the energy density is necessarily negative and the fluid distribution…
Stable numerical simulations for a hyperbolic system of conservation laws of relaxation type but not in divergence form are obtained by incorporating the physical entropy into the simulations. The entropy balance is utilized as an…
Conservation equations for the mass, linear momentum and energy densities of solitons propagating in finite, infinite and periodic, nonlinear, planar waveguides and governed by the nonlinear Schr\"odinger equation are derived. These…
A quantum system at equilibrium is represented by a corresponding classical system, chosen to reproduce thermodynamic and structural properties. The motivation is to allow application of classical strong coupling theories and molecular…
In this paper, we revise Maxwell's constitutive relation and formulate a system of first-order partial differential equations with two parameters for compressible viscoelastic fluid flows. The system is shown to possess a nice…
We propose a system of conservation laws with relaxation source terms (i.e. balance laws) for non-isothermal viscoelastic flows of Maxwell fluids. The system is an extension of the polyconvex elastodynamics of hyperelastic bodies using…
We study a general convergence theory for the numerical solutions of compressible viscous and electrically conducting fluids with a focus on numerical schemes that preserve the divergence free property of magnetic field exactly. Our…
The existing paradox between theory and computational experiment for weak solutions of systems of conservation laws in higher space dimensions is arguably resolved. Apparently successful computations are identified with underlying…
Motivated by the initial-boundary value problem for the Einstein equations, we propose a definition of symmetric hyperbolicity for systems of evolution equations that are first order in time but second order in space. This can be used to…
The purpose of this paper is to deal with the issue of well-posedness for a class of non-Newtonian fluid dynamics equations. These sets of equations are commonly used to describe various complex models that appear in nature, industry, and…
Switched linear hyperbolic partial differential equations are considered in this paper. They model infinite dimensional systems of conservation laws and balance laws, which are potentially affected by a distributed source or sink term. The…
A complete classification of all low-order conservation laws is carried out for a system of coupled semilinear wave equations which is a natural two-component generalization of the nonlinear Klein-Gordon equation. The conserved quantities…
An algorithm is constructed which allows to express conserved flows of hyperbolic equations in terms of corresponding conserved densities and to eliminate these flows from conservation laws of hyperbolic equations. The application of this…