相关论文: Construction of potential systems for systems of P…

We construct stochastic multisymplectic systems by considering a stochastic extension to the variational formulation of multisymplectic partial differential equations proposed in [Hydon, {\it Proc. R. Soc. A}, 461, 1627--1637, 2005]. The…

We establish that stabilization of a class of linear, hyperbolic partial differential equations (PDEs) with a large (nevertheless finite) number of components, can be achieved via employment of a backstepping-based control law, which is…

We study local conservation laws of variable coefficient diffusion-convection equations of the form $f(x)u_t=(g(x)A(u)u_x)_x+h(x)B(u)u_x$. The main tool of our investigation is the notion of equivalence of conservation laws with respect to…

We show that, under suitable conditions, finite-dimensional systems describing invariant solutions of partial differential equations (PDEs) inherit local Hamiltonian operators through the mechanism of invariant reduction, which applies…

We consider energetics and structural properties of a many particle system in one dimension with pairwise contact interactions confined in a parabolic external potential. To render the problem analytically solvable, we use the harmonic…

We discuss a systematic construction of dimensionless quantum-mechanical equations. The process reduces the number of independent model parameters to a minimum and, at the same time, provides the natural units of length, energy, etc. in a…

Conservation laws are discussed in conjunction with quantum-mechanical indeterminacies of the corresponding observables. The considered examples show that the connections between energy and its indeterminacy may be quite intricate. The…

Symmetry groups of PDEs allow to transform solutions continuously into other solutions. In this paper, we use this property for the observability analysis of nonlinear PDEs with input and output. Based on a differential-geometric…

We propose reducible algebraic curves as a mechanism to construct Partial MDS (PMDS) codes geometrically. We obtain new general existence results, new explicit constructions and improved estimates on the smallest field sizes over which such…

Comparison principles are developed for discrete quasilinear elliptic partial differential equations. We consider the analysis of a class of nonmonotone Leray-Lions problems featuring both nonlinear solution and gradient dependence in the…

The paper develops the method for construction of the families of particular solutions to the nonlinear Partial Differential Equations (PDE) without relation to the complete integrability. Method is based on the specific link between…

The Poisson structures for 3D systems possessing one constant of motion can always be constructed from the solution of a linear PDE. When two constants of the motion are available the problem reduces to a quadrature and the structure…

This paper is concerned with linear parameter-dependent systems and considers the notion uniform ensemble reachability. The focus of this work is on constructive methods to compute suitable parameter-independent open-loop inputs for such…

We use partial differential equations (PDEs) to describe physical systems. In general, these equations include evolution and constraint equations. One method used to find solutions to these equations is the Free-evolution approach, which…

Partial differential equations with discrete (concentrated) state-dependent delays are studied. The existence and uniqueness of solutions with initial data from a wider linear space is proven first and then a subset of the space of…

Previous studies have used numerical methods to optimize the hyperpolarizability of a one-dimensional quantum system. These studies were used to suggest properties of one-dimensional organic molecules, such as the degree of modulation of…

In this work we propose a new, arbitrary order space-time finite element discretisation for Hamiltonian PDEs in multisymplectic formulation. We show that the new method which is obtained by using both continuous and discontinuous…

Nonlocal conservation laws are used to describe various realistic instances of crowd behaviors. First, a basic analytic framework is established through an "ad hoc" well posedness theorem for systems of nonlocal conservation laws in several…

Aggregation processes with an arbitrary number of conserved quantities are investigated. On the mean-field level, an exact solution for the size distribution is obtained. The asymptotic form of this solution exhibits nontrivial ``double''…

The reduction of dynamical systems has a rich history, with many important applications related to stability, control and verification. Reduction of nonlinear systems is typically performed in an exact manner - as is the case with…