Related papers: Hierarchies of N-Point Functions for Nonlinear Con…
We consider conservation laws with nonlocal velocity and show for nonlocal weights of exponential type that the unique solutions converge in a weak or strong sense (dependent on the regularity of the velocity) to the entropy solution of the…
Scalar conservation laws sit at the intersection between being simple enough to study analytically, while being complex enough to exhibit a wide range of nonlinear phenomena. We introduce a novel stochastic perturbation of scalar…
In this article, we present a method to find a solution to a one-dimensional nonlocal conservation law that respects a space-dependent mapping, referred to as the obstacle. This is achieved by generalizing existing results for the local…
This paper investigates the existence of solutions for a class of nonlinear higher-order dynamic equations subject to mixed boundary conditions. We consider boundary value problems in which the nonlinear reaction functions satisfy…
In (Nucci M.C. 1994, Physica D 78 p.124), we have found that iterations of the nonclassical symmetries method give rise to new nonlinear equations, which inherit the Lie point symmetry algebra of the given equation. In the present paper, we…
The idea of using fast sweeping methods for solving stationary systems of conservation laws has previously been proposed for efficiently computing solutions with sharp shocks. We further develop these methods to allow for a more challenging…
Non-Hermitian systems can manifest rich static and dynamical properties at their exceptional points (EPs). Here, we identify yet another class of distinct phenomena that is hinged on EPs, namely, the emergence of a series of non-Hermitian…
We present a stochastic, time-discrete boolean model which mimics the mesoscopic dynamics of the desorption reactions $A+A\to A+S$ and $A+A\to S+S$ in a 1D lattice. In the continuous-time limit, we derive a hierarchy of dynamical equations…
A didactic and systematic derivation of Noether point symmetries and conserved currents is put forward in special relativistic field theories, without a priori assumptions about the transformation laws. Given the Lagrangian density, the…
We analyze Non-linear chaffee infatne equation by groups theoretical method to get its symmetries and conservation laws.
We investigate real solutions of a C-integrable non-evolutionary partial differential equation in the form of a scalar conservation law where the flux density depends both on the density and on its first derivatives with respect to the…
We develop deterministic particle schemes to solve non-local scalar conservation laws with congestion. We show that the discrete approximations converge to the unique entropy solution with an explicit rate of convergence under more general…
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…
In this contribution, we present a novel approach for solving the obstacle problem for (linear) conservation laws. Usually, given a conservation law with an initial datum, the solution is uniquely determined. How to incorporate obstacles,…
We investigate the evolution of localized initial value profiles when propagated in integrable versions of higher time-derivative theories. In contrast to the standard cases in nonlinear integrable systems, where these profiles evolve into…
Sequences of random objects arise from many real applications, including high throughput omic data and functional imaging data. Those sequences are usually dependent, non-linear, or even Non-Euclidean, and an important problem is…
In this article, we present an extension of the splitting algorithm proposed in [22] to networks of conservation laws with piecewise linear discontinuous flux functions in the unknown. We start with the discussion of a suitable Riemann…
This article studies the Cauchy problem for the scalar conservation law \[ \partial_t u + \partial_t w + \partial_x f(u) = 0, \] where $w(x,t) = [\mathcal{F}(u)(x,t)]$ is the output of a specific hysteresis operator, namely the Play…
We consider solutions of two-dimensional $m \times m$ systems hyperbolic conservation laws that are constant in time and along rays starting at the origin. The solutions are assumed to be small $L^\infty$ perturbations of a constant state…
This paper deals with the existence of solutions to a class of fourth order nonlinear elliptic equations. The technique used relies on critical points theory. The solutions appeared as critical points of a functional restricted to a…