Related papers: Conservation Laws for $p$-Harmonic Systems with An…
Some of recent important developments are overviewed, several longstanding open problems are discussed, and a perspective is presented for the mathematical theory of multidimensional conservation laws. Some basic features and phenomena of…
We develop a general framework for the analysis of approximations to stochastic scalar conservation laws. Our aim is to prove, under minimal consistency properties and bounds, that such approximations are converging to the solution to a…
A case can be made that the utility of quasi-linear systems of conservation laws as physical models is largely limited to Euler system models of fluid flow, at least in higher dimensions. Qualified corroboration of this conjecture is…
Nonlinear generalizations of integrable equations in one dimension, such as the KdV and Boussinesq equations with $p$-power nonlinearities, arise in many physical applications and are interesting in analysis due to critical behaviour. This…
Symmetry, which describes invariance, is an eternal concern in mathematics and physics, especially in the investigation of solutions to the partial differential equation (PDE). A PDE's nonlocally related PDE systems provide excellent…
Two-component second and third-order Burgers type systems with nondiagonal constant matrix of leading order terms are classified for higher symmetries. New symmetry integrable systems with their master symmetries are obtained. Some third…
This work extends the Ibragimov's conservation theorem for partial differential equations [{\it J. Math. Anal. Appl. 333 (2007 311-328}] to under determined systems of differential equations. The concepts of adjoint equation and formal…
We provide an elementary proof of geometric synchronisation for scalar conservation laws on a domain with Dirichlet boundary conditions. Unlike previous results, our proof does not rely on a strict maximum principle, and builds instead on a…
This paper deals with diffusive limit of the p-system with damping and its approximation by an Asymptotic Preserving (AP) Finite Volume scheme. Provided the system is endowed with an entropy-entropy flux pair, we give the convergence rate…
In this note a new way to construct the characteristics of conservations laws of integrable chiral-type systems is proposed.
Historically it happen so that in branches of physics connected with field theory and of physics of material systems (continuous media) the concept of "conservation laws" has a different meaning. In field theory "conservation laws" are…
We revisit the work studying homomorphism preservation for first-order logic in sparse classes of structures initiated in [Atserias et al., JACM 2006] and [Dawar, JCSS 2010]. These established that first-order logic has the homomorphism…
This two-part article considers certain fundamental symmetries of nature, namely the discrete symmetries of parity (P), charge conjugation (C) and time reversal (T), and their possible violation. Recent experimental results are discussed in…
New nonlocal symmetries and conservation laws are derived for Maxwell's equations using a covariant system of joint vector potentials for the electromagnetic tensor field and its dual. A key property of this system, as well as of this class…
A variant of the divergence theory for vacuum-condensation developed in a previous communication is analyzed from the viewpoint of a 'time' asymmetric law in vacuum. This law is found to establish a substantial distinction between…
We prove that under certain assumptions a partial differential equation can be derived from a variational principle. It is well-known from Noether's theorem that symmetries of a variational functional lead to conservation laws of the…
This two-part article considers certain fundamental symmetries of nature, namely the discrete symmetries of parity (P), charge conjugation (C) and time reversal (T), and their possible violation. Recent experimental results are discussed in…
We propose a new notion called \emph{infinity-harmonic maps}between Riemannain manifolds. These are natural generalizations of the well known notion of infinity harmonic functions and are also the limiting case of $p$% -harmonic maps as…
In the present paper geometric aspects of relationship between non-Noether symmetries and conservation laws in Hamiltonian systems is discussed. It is shown that integrals of motion associated with continuous non-Noether symmetry are in…
We analyze the optical properties of one-dimensional (1D) PT-symmetric structures of arbitrary complexity. These structures violate normal unitarity (photon flux conservation) but are shown to satisfy generalized unitarity relations, which…