Related papers: Conservation Laws With Random and Deterministic Da…
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…
We consider conservation laws with source terms in a bounded domain with Dirichlet boundary conditions. We first prove the existence of a strong trace at the boundary in order to provide a simple formulation of the entropy boundary…
In an earlier work by a subset of the present authors, the method of the so-called neural deflation was introduced towards identifying a complete set of functionally independent conservation laws of a nonlinear dynamical system. Here, we…
In the work it has been shown that there are two types of the conservation laws. 1. The conservation laws that can be called exact ones. They point to an avalability of some conservative quantities or objects. Such objects are the physical…
The discrete nonlinear Schr\"odinger equation on \(\Z^d\), \(d \geq 1\) is an example of a dispersive nonlinear wave system. Being a Hamiltonian system that conserves also the \(\ell^2(\Z^d)\)-norm, the well-posedness of the corresponding…
We review models of biological evolution in which the population frequency changes deterministically with time. If the population is self-replicating, although the equations for simple prototypes can be linearised, nonlinear equations arise…
We consider entropy conservative and dissipative discretizations of nonlinear conservation laws with implicit time discretizations and investigate the influence of iterative methods used to solve the arising nonlinear equations. We show…
Conserved quantities increasingly underpin the inference of physical models. Recently new conserved quantities have been found in this context, that currently lack an interpretation. Here, we show that irreversible reactions in CRNs and…
In this paper hyperbolic partial differential equations with random coefficients are discussed. We consider the challenging problem of flux functions with coefficients modeled by spatiotemporal random fields. Those fields are given by…
The notions of generating sets of conservation laws of systems of differential equations with respect to symmetry groups and equivalence groups are introduced and applied. This allows us to generalize essentially the procedure of finding…
Making sense of complex inhomogeneous systems composed of many interacting species is a grand challenge that pervades basically all natural sciences. Phase separation and pattern formation in reaction-diffusion systems have been largely…
We propose a novel approach in the study of transport phenomena in dense systems or systems with long range interactions where multiple particle interactions must be taken into consideration. Within Boltzmann's kinetic formalism, we study…
Time-dependent models of fluid motion in thin layers, subject to signed source terms, represent important sub-problems within climate dynamics. Examples include ice sheets, sea ice, and even shallow oceans and lakes. We address these…
Partial differential equations (PDEs) describing thermodynamically isolated systems typically possess conserved quantities (like mass, momentum, and energy) and dissipated quantities (like entropy). Preserving these conservation and…
A direct method for the computation of polynomial conservation laws of polynomial systems of nonlinear partial differential equations (PDEs) in multi-dimensions is presented. The method avoids advanced differential-geometric tools. Instead,…
Energy methods for constructing time-stepping algorithms are of increased interest in application to nonlinear problems, since numerical stability can be inferred from the conservation of the system energy. Alternatively, symplectic…
Infinite order differential equations have come to play an increasingly significant role in theoretical physics. Field theories with infinitely many derivatives are ubiquitous in string field theory and have attracted interest recently also…
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…
Motivated by the statistical description of turbulence, we study statistical conservation laws in the form of kinetic-type PDEs for joint probability density functions (PDFs) and cumulative distribution functions (CDFs) associated with…
We develop a rigorous theory of external influences on finite discrete dynamical systems, going beyond the perturbation paradigm, in that the external influence need not be a small contribution. Indeed, the covariance condition can be…