Scalar conservation laws with white noise initial data
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DOI: 10.1007/s00440-021-01083-z
Abstract: The statistical description of the scalar conservation law of the form $\rho_t=H(\rho)_x$ with $H: \mathbb{R} \rightarrow \mathbb{R}$ a smooth convex function has been an object of interest when the initial profile $\rho(\cdot,0)$ is random. The… read more here.
Keywords: conservation laws; laws white; scalar conservation; white noise ... See more keywords
Finite Time Emergence of A Shock Wave for Scalar Conservation Laws Via Lax-Oleinik Formula
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DOI: 10.1007/s10473-019-0107-8
Abstract: In this paper, we use Lax-Oleinik formula to study the asymptotic behavior for the initial problem of scalar conservation law ut + F(u)x = 0. First, we prove a simple but useful property of Lax-Oleinik… read more here.
Keywords: shock; scalar conservation; oleinik formula; lax oleinik ... See more keywords
Scalar conservation laws: Initial and boundary value problems revisited and saturated solutions
Sign Up to like & getrecommendations! Published in 2018 at "Comptes Rendus Mathematique"
DOI: 10.1016/j.crma.2018.09.010
Abstract: Abstract We revisit the classical theory of multidimensional scalar conservation laws. We reformulate the notion of the classical Kruzkov entropy solutions and study some new properties as well as the well-posedness of the initial value… read more here.
Keywords: scalar conservation; value; boundary value; conservation laws ... See more keywords
Riemann problem for the 2D scalar conservation law involving linear fluxes with discontinuous coefficients
Sign Up to like & getrecommendations! Published in 2020 at "Journal of Mathematical Physics"
DOI: 10.1063/5.0022048
Abstract: This paper is devoted to the four-constant Riemann problem for the two-dimensional (2D) scalar conservation laws involving linear fluxes with discontinuous coefficients. First, under the assumption that each discontinuity ray of initial data outside of… read more here.
Keywords: linear fluxes; scalar conservation; riemann problem; involving linear ... See more keywords
Convergence rates toward shock profiles for scalar conservation laws with nonlinear viscosity
Sign Up to like & getrecommendations! Published in 2025 at "Applicable Analysis"
DOI: 10.1080/00036811.2025.2489465
Abstract: We are interested in the large time behavior of solutions to a scalar conservation law with nonlinear viscosity, which models a non-Newtonian incompressible fluid with power-law type viscosity. The asymptotic stability of viscous shock waves… read more here.
Keywords: scalar conservation; nonlinear viscosity; convergence rates; shock ... See more keywords
Decay of Unstable Strong Discontinuities in the Case of a Convex-Flux Scalar Conservation Law Approximated by the CABARET Scheme
Sign Up to like & getrecommendations! Published in 2018 at "Computational Mathematics and Mathematical Physics"
DOI: 10.1134/s0965542518060155
Abstract: Monotonicity conditions for the CABARET scheme approximating a quasilinear scalar conservation law with a convex flux are obtained. It is shown that the monotonicity of the CABARET scheme for Courant numbers $$r \in (0.5,1]$$ does… read more here.
Keywords: scalar conservation; decay unstable; strong discontinuities; unstable strong ... See more keywords
The arbitrary-order fractional hyperbolic nonlinear scalar conservation law
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DOI: 10.1186/s13662-020-02697-8
Abstract: In this paper, we use a new powerful technique of arbitrary-order fractional (AOF) characteristic method (CM) to solve the AOF hyperbolic nonlinear scalar conservation law (HNSCL) of time and space. We present the existence and… read more here.
Keywords: order; scalar conservation; hyperbolic nonlinear; nonlinear scalar ... See more keywords