相关论文: Higher regularity for entropy solutions of conserv…
This article deals with the error estimates for numerical approximations of the entropy solutions of coupled systems of nonlocal hyperbolic conservation laws. The systems can be strongly coupled through the nonlocal coefficient present in…
The dynamics of nonlinear conservation laws have long posed fascinating problems. With the introduction of some nonlinearity, e.g. Burgers' equation, discontinuous behavior in the solutions is exhibited, even for smooth initial data. The…
In this paper we analyze the long-time behavior of solutions to conservation laws with nonlinear diffusion terms of different types: saturating dissipation (monotone and non monotone) and singular nonlinear diffusions are considered. In…
We study the following class of scalar hyperbolic conservation laws with discontinuous fluxes: \partial_t\rho+\partial_xF(x,\rho)=0. The main feature of such a conservation law is the discontinuity of the flux function in the space variable…
We prove the stability of entropy solutions of nonlinear conservation laws with respect to perturbations of the initial datum, the space-time dependent flux and the entropy inequalities. Such a general stability theorem is motivated by the…
We establish a general nonlocal approximation principle for the entropy solutions of scalar conservation laws on $\mathbb{R}$. More precisely, we show that the entropy solution to a nonnegative initial datum can be obtained as a weak-star…
The SBV regularity of weak entropy solutions to the Burgers-Poisson equation is considered. We show that the derivative of a solution consists of only the absolutely continuous part and the jump part.
We obtain solutions to conservation laws under any random initial conditions that are described by Gaussian stochastic processes (in some cases discretized). We analyze the generalization of Burgers' equation for a smooth flux function…
In this paper, we propose new spectral viscosity methods based on the generalized Hermite functions for the solution of nonlinear scalar conservation laws in the whole line. It is shown rigorously that these schemes converge to the unique…
We study nonlocal conservation laws with a discontinuous flux function of regularity $\mathsf{L}^{\infty}(\mathbb{R})$ in the spatial variable and show existence and uniqueness of weak solutions in…
We are concerned with multidimensional stochastic balance laws. We identify a class of nonlinear balance laws for which uniform spatial $BV$ bounds for vanishing viscosity approximations can be achieved. Moreover, we establish temporal…
In this work we consider companion conservation laws to general systems of conservation laws. We investigate sufficient regularity for weak solutions to satisfy companion laws, assuming the fluxes to be $C^{1,\gamma}$, $0<\gamma<1$,…
We introduce the notion of entropy solutions (e.s.) to a conservation law with an arbitrary jump continuous flux vector and prove existence of the largest and the smallest e.s. to the Cauchy problem. The monotonicity and stability…
We study a class of variational problems for regularized conservation laws with Lax's entropy-entropy flux pairs. We first introduce a modified optimal transport space based on conservation laws with diffusion. Using this space, we…
Nonlinear conservation laws such as the system of ideal magnetohydrodynamics (MHD) equations may develop singularities over time. In these situations, viscous regularization is a common approach to regain regularity of the solution. In this…
We found the precise condition for the decay as $t\to\infty$ of Besicovitch almost periodic entropy solutions of multidimensional scalar conservation laws. Moreover, in the case of one space variable we establish asymptotic convergence of…
This document provides a proof that the solutions to the convectively filtered Burgers equation, will converge to the entropy solution of the inviscid Burgers equation when certain restrictions are put on the initial conditions. It does so…
Under a precise genuine nonlinearity assumption we establish the decay of entropy solutions of a multidimensional scalar conservation law with merely continuous flux.
Reduced order models of nonlinear conservation laws in fluid dynamics do not typically inherit stability properties of the full order model. We introduce projection-based hyper-reduced models of nonlinear conservation laws which are…
We develop a discretely entropy-stable line-based discontinuous Galerkin method for hyperbolic conservation laws based on a flux differencing technique. By using standard entropy-stable and entropy-conservative numerical flux functions,…