Related papers: Optimal Regularizing Effect for Scalar Conservatio…
We prove the convergence of the explicit-in-time Finite Volume method with monotone fluxes for the approximation of scalar first-order conservation laws with multiplicative, compactly supported noise.
Schaeffer's regularity theorem for scalar conservation laws can be loosely speaking formulated as follows. Assume that the flux is uniformly convex, then for a generic smooth initial datum the admissible solution is smooth outside a locally…
In this work, we modify a continuous Galerkin discretization of a scalar hyperbolic conservation law using new algebraic correction procedures. Discrete entropy conditions are used to determine the minimal amount of entropy stabilization…
We propose new entropy admissibility conditions for multidimensional hyperbolic scalar conservation laws with discontinuous flux which generalize one-dimensional Karlsen-Risebro-Towers entropy conditions. These new conditions are designed,…
We show that weak solutions of general conservation laws in bounded domains conserve their generalized entropy, and other respective companion laws, if they possess a certain fractional differentiability of order 1/3 in the interior of the…
We consider degenerate and singular parabolic equations with $p$-Laplacian structure in bounded nonsmooth domains when the right-hand side is a signed Radon measure with finite total mass. We develop a new tool that allows global regularity…
We prove that adapted entropy solutions of scalar conservation laws with discontinuous flux are stable with respect to changes in the flux under the assumption that the flux is strictly monotone in u and the spatial dependency is piecewise…
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…
The paper deals with scalar conservation laws having a flux discontinuity at $x=0$ without a weak solution that satisfies the classical Rankine--Hugoniot jump condition at $x=0$. We are using unbounded solutions in the form of shadow waves…
We study compactness properties of time-discrete and continuous time BGK-type schemes for scalar conservation laws, in which microscopic interactions occur only when the state of a system deviates significantly from an equilibrium…
In this paper, we study a scalar conservation law that models a highly re-entrant manufacturing system as encountered in semi-conductor production. As a generalization of \cite{CKWang}, the velocity function possesses both the local and…
We consider a planar viscous shock for a scalar viscous conservation law with a strictly convex flux in multi-dimensional setting, where the transversal direction is periodic. We first show the contraction property for any solutions…
In this note we discuss the SBV-regularity for a scalar balance law in one space dimension as a case study in order to explain the strategy that we apply in a separate paper to general hyperbolic systems of balance laws in one space…
An "exact" method for scalar one-dimensional hyperbolic conservation laws is presented. The approach is based on the evolution of shock particles, separated by local similarity solutions. The numerical solution is defined everywhere, and is…
Aim of this paper is to review some basic ideas and recent developments in the theory of strictly hyperbolic systems of conservation laws in one space dimension. The main focus will be on the uniqueness and stability of entropy weak…
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…
Classifications of symmetries and conservation laws are presented for a variety of physically and analytically interesting wave equations with power onlinearities in n spatial dimensions: a radial hyperbolic equation, a radial Schrodinger…
This paper establishes the ergodicity in $H^\nn,\nn=\lfloor\frac{d}{2}+1\rfloor$ of the viscous scalar conservation laws on torus $\mT^d$ with general polynomial flux and a degenerate noise. The noise could appear in as few as several…
We consider nondecreasing entropy solutions to 1-d scalar conservation laws and show that the spatial derivatives of such solutions satisfy a contraction property with respect to the Wasserstein distance of any order. This result extends…
We prove that vanishing viscosity solutions to smooth non-degenerate systems of balance laws having small bounded variation, in one space dimension, must be functions of special bounded variation. For more than one equation, this is new…