相关论文: An Interesting Class of Partial Differential Equat…

The past decades have seen increasing interest in modelling uncertainty by heterogeneous methods, combining probability and interval analysis, especially for assessing parameter uncertainty in engineering models. A unifying mathematical…

Extremal principles can generally be divided into two rather distinct classes. There are, on the one hand side, formulations based on the Lagrangian or Hamiltonian mechanics, respectively, dealing with time dependent problems, but…

In this master's thesis, we rigorously develop two frameworks of relational composition of systems using tools from category theory. The first framework addresses port-Hamiltonian systems, which are dynamical systems whose dynamics are…

The geometrical theory of partial differential equations in the absolute sense, without any additional structures, is developed. In particular the symmetries need not preserve the hierarchy of independent and dependent variables. The order…

We define the notion of localizable property for a dynamical system. Then we survey three properties of complexity and relate how they are known to be typical among differentiable dynamical systems. These notions are the fast growth of the…

We prove the equivalence among symmetricity, time reversibility, and zero entropy production of the stationary solutions of linear stochastic differential equations. A sufficient and necessary reversibility condition expressed in terms of…

This paper is concerned with boundary stabilization of two-dimensional hyperbolic systems of partial differential equations. By adapting the Lyapunov function previously proposed by the second author for linearized hyperbolic systems with…

A system can be driven out of equilibrium by both time-dependent and nonconservative forces, which gives rise to a decomposition of the dissipation into two non-negative components, called the excess and housekeeping entropy productions. We…

For the fractional Laplace equation, a surprising observation is the non-uniqueness for the basic Dirichlet type problems. In this paper, a somewhat sharp uniqueness condition for the fractional Laplace equation is established. We derive…

The dynamics of the fluid fields in a large class of causal dissipative fluid theories is studied. It is shown that the physical fluid states in these theories must relax (on a time scale that is characteristic of the microscopic particle…

We formulate the 2-body problem of electrodynamics using functional differential equations, and explain the peculiar features of these equations which indicate a paradigm shift in physics. We examine the possible empirical existence of…

We derive thermodynamically consistent models of reaction-diffusion equations coupled to a heat equation. While the total energy is conserved, the total entropy serves as a driving functional such that the full coupled system is a gradient…

Differential properties for orthogonal polynomials in several variables are studied. We consider multivariate orthogonal polynomials whose gradients satisfy some quasi--orthogonality conditions. We obtain several characterizations for these…

We consider a very complicated system of some latticized differential equations that is considered as equations of motion for a field theory. We define macro state restrictions for such a system analogous to thermodynamical states of a…

In this effort we show that the Legendre reciprocity relations,thermodynamic's essential formal feature, are respected by any entropic functional, even if it is NOT of trace-form nature, as Shannon's is. Further, with reference to the…

We show that weak solutions of general conservation laws in bounded domains conserve their generalized entropy, and other respective companion laws, if they possess a certain fractional differentiability of order 1/3 in the interior of the…

Starting from the entropy production being invariant under time reversal, one can (i) easily proof, and understand, many aspects of the linear Onsager relations and (ii) deduce the result that all quadratic Onsager coefficients for…

In this work we study the properties of a relativistic mixture of two non-reacting dilute species in thermal local equilibrium. Following the conventional ideas in kinetic theory, we use the concept of chaotic velocity. In particular, we…

We study holographic entropy inequalities and their structural properties by making use of a judicious grouping of terms into certain multipartite information quantities. This allows us to recast cumbersome entropic expressions into much…

We show how dynamical equations for liquid films and drops on uneven surfaces, including contact line dynamics and evaporation/condensation effects, may be formulated as a variational dynamics, generated via Onsager's variational principle.…