We introduce a variational principle for field theories, referred to as the HamiltonPontryagin principle, and we show that the resulting field equations are the Euler-Lagrange equations in implicit form. Secondly, we introduce multi-Dirac structures as a graded analog of standard Dirac structures, and we show that the graph of a multisymplectic form determines a multi-Dirac structure. We then d...

The paper formulates a statement of the problem and develops mathematical models deformation underground pipelines under spatially variable loading, taking into account accumulation damageability materials. Based on theory small elasto-plastic deformations Hamilton-Ostrogradsky variational principle, differential equations motion (equilibrium) system alternating loading with appropriate boundar...

In this work, we propose a high-resolution alternating evolution (AE) scheme to solve Hamilton–Jacobi equations. The construction of the AE scheme is based on an alternating evolution system of the Hamilton–Jacobi equation, following the idea previously developed for hyperbolic conservation laws. A semidiscrete scheme derives directly from a sampling of this system on alternating grids. Higher ...

We study discounted Hamilton Jacobi equations on networks, without putting any restriction their geometry. Assuming the Hamiltonians continuous and coercive, we establish a comparison principle provide representation formulae for solutions. follow approach introduced in 11, namely associate to differential problem network, discrete functional equation an abstract underlying graph. perform some ...

We consider a stochastic transportation problem between two prescribed probability distributions (a source and target) over processes with general drift dependence free end times. First, in order to establish dual principle, we associate equivalent formulations of the primal guarantee its convexity lower semi-continuity respect target distributions. exhibit an Eulerian formulation, whose variat...

Advanced methods of theory of optimal guaranteeing control and techniques of generalized (viscosity, minimax) solutions of Hamilton-Jacobi equations are applied to nonzero sum game interaction between two large groups (coalitions) of agents (participants) arising in economic and biological evolutionary models. Random contacts of agents from different groups happen according to a control dynamic...

We present an alternative nonconservative gravitational theory based on the Herglotz variational principle in a fully covariant form. The model may be seen as improvement of proposed Ref. [Lazo et al, Phys. Rev. D 95, 101501 (2017)], whose resulting is meaningful just particular coordinate systems. In work, we report new that free from such restriction. It also obtained using and by taking adva...

We study the Hamilton-Jacobi equations $H(x,Du,u)=0$ in $M$ and $\partial u/\partial t +H(x,D_xu,u)=0$ $M\times(0,\infty)$, where Hamiltonian $H=H(x,p,u)$ depends Lipschitz continuously on variable $u$. In framework of semicontinuous viscosity solutions due to Barron-Jensen, we establish comparison principle, existence theorem, representation formula as value functions for extended real-valued,...

This paper presents a mathematical model of an electric power system which consists three-phase line with distributed parameters and equivalent, unbalanced RLC load cooperating the line. The above was developed on basis modified Hamilton–Ostrogradsky principle, extends classical Lagrangian by adding two more components: energy dissipative forces in work external non-conservative forces. In mode...